The free idempotent generated locally inverse semigroup

Oliveira, Luís

doi:10.1007/s00233-017-9882-5

Cited by 5 publications

(1 citation statement)

References 18 publications

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“…Many important subclasses of regular semigroups (for example, completely regular semigroups, inverse semigroups, orthodox semigroups, locally inverse semigroups, etc.) (see [13][14][15][16][17][18][19][20][21][22]) have been proposed one after another, and their structures have been deeply revealed. In particular, as a group union semigroup, completely regular semigroups have been deeply studied and widely used, and have become the most wonderful content of regular semigroups.…”

Section: Introductionmentioning

confidence: 99%

Left (Right) Regular and Transposition Regular Semigroups and Their Structures

Zhang

2022

Mathematics

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Regular semigroups and their structures are the most wonderful part of semigroup theory, and the contents are very rich. In order to explore more regular semigroups, this paper extends the relevant classical conclusions from a new perspective: by transforming the positions of the elements in the regularity conditions, some new regularity conditions (collectively referred to as transposition regularity) are obtained, and the concepts of various transposition regular semigroups are introduced (L1/L2/L3, R1/R2/R3-transposition regular semigroups, etc.). Their relations with completely regular semigroups and left (right) regular semigroups, proposed by Clifford and Preston, are analyzed. Their properties and structures are studied from the aspects of idempotents, local identity elements, local inverse elements, subsemigroups and so on. Their decomposition theorems are proved respectively, and some new necessary and sufficient conditions for semigroups to become completely regular semigroups are obtained.

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Section: Introductionmentioning

confidence: 99%

Left (Right) Regular and Transposition Regular Semigroups and Their Structures

Zhang

2022

Mathematics

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The Mathematical Work of K. S. S. Nambooripad

Meakin

Muhammed

Rajan

2021

Springer Proceedings in Mathematics &Amp; Statistics

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Cross-connection structure of locally inverse semigroups

Muhammed

Volkov

Auinger

2022

Int. J. Algebra Comput.

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Locally inverse semigroups are regular semigroups whose idempotents form pseudo-semilattices. We characterize the categories that correspond to locally inverse semigroups in the realm of Nambooripad’s cross-connection theory. Further, we specialize our cross-connection description of locally inverse semigroups to inverse semigroups and completely [Formula: see text]-simple semigroups, obtaining structure theorems for these classes. In particular, we show that the structure theorem for inverse semigroups can be obtained using only one category, quite analogous to the Ehresmann–Schein–Nambooripad Theorem; for completely [Formula: see text]-simple semigroups, we show that cross-connections coincide with structure matrices, thus recovering the Rees Theorem by categorical tools.

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The free idempotent generated locally inverse semigroup

Cited by 5 publications

References 18 publications

Left (Right) Regular and Transposition Regular Semigroups and Their Structures

Left (Right) Regular and Transposition Regular Semigroups and Their Structures

The Mathematical Work of K. S. S. Nambooripad

Cross-connection structure of locally inverse semigroups

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