20Mxx Semigroups
This subtopic studies semigroups, examining associative binary operations without inverses and the algebraic structure that arises from them.
Specific topics
20M05 Free semigroups, generators and relations, word problems
Overview
20M05 studies free semigroups, generators and relations, word problems in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for free semigroups, generators and relations, word problems
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M07 Varieties and pseudovarieties of semigroups
Overview
20M07 studies varieties and pseudovarieties of semigroups in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for varieties and pseudovarieties of semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M10 General structure theory for semigroups
Overview
20M10 studies general structure theory for semigroups in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general structure theory for semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M12 Ideal theory for semigroups
Overview
20M12 studies ideal theory for semigroups in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for ideal theory for semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M13 Arithmetic of semigroups
Overview
20M13 studies arithmetic of semigroups in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for arithmetic of semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M14 Commutative semigroups
Overview
20M14 studies commutative semigroups in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for commutative semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M15 Mappings of semigroups
Overview
20M15 studies mappings of semigroups in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for mappings of semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M17 Regular semigroups
Overview
20M17 studies regular semigroups in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for regular semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M18 Inverse semigroups
Overview
20M18 studies inverse semigroups in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for inverse semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M19 Orthodox semigroups
Overview
20M19 studies orthodox semigroups in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for orthodox semigroups
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M20 Semigroups of transformations, relations, partitions
Overview
20M20 studies semigroups of transformations, relations, partitions in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for semigroups of transformations, relations, partitions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M25 Semigroup rings, multiplicative semigroups of rings
Overview
20M25 studies semigroup rings, multiplicative semigroups of rings in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for semigroup rings, multiplicative semigroups of rings
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M30 Representation of semigroups; actions of semigroups on sets
Overview
20M30 studies representation of semigroups; actions of semigroups on sets in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for representation of semigroups; actions of semigroups on sets
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M32 Algebraic monoids
Overview
20M32 studies algebraic monoids in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for algebraic monoids
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M35 Semigroups in automata theory, linguistics, etc.
Overview
20M35 studies semigroups in automata theory, linguistics, etc. in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for semigroups in automata theory, linguistics, etc.
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M50 Connections of semigroups with homological algebra
Overview
20M50 studies connections of semigroups with homological algebra in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for connections of semigroups with homological algebra
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks
20M99 None of the above
Overview
20M99 studies none of the above in semigroups. It studies associative binary operations without inverses, with emphasis on structure theory, presentations, and special classes.
Related Wikipedia Page
Semigroups (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for none of the above
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in automata theory, combinatorics, and the algebraic study of transformations.
Applications
- Semigroup structure and ideals
- Inverse and regular semigroups
- Automata-theoretic and combinatorial applications
References
Recommended Textbooks