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Cross-connection structure of locally inverse semigroups. / Azeef Muhammed, P. A.; Volkov, Mikhail V.; Auinger, Karl.
In: International Journal of Algebra and Computation, Vol. 33, No. 01, 01.02.2023, p. 123-159.

Research output: Contribution to journal › Article › peer-review

Harvard

Azeef Muhammed, PA, Volkov, MV & Auinger, K 2023, 'Cross-connection structure of locally inverse semigroups', International Journal of Algebra and Computation, vol. 33, no. 01, pp. 123-159. https://doi.org/10.1142/S0218196723500091

APA

Azeef Muhammed, P. A., Volkov, M. V., & Auinger, K. (2023). Cross-connection structure of locally inverse semigroups. International Journal of Algebra and Computation, 33(01), 123-159. https://doi.org/10.1142/S0218196723500091

Vancouver

Azeef Muhammed PA, Volkov MV, Auinger K. Cross-connection structure of locally inverse semigroups. International Journal of Algebra and Computation. 2023 Feb 1;33(01):123-159. doi: 10.1142/S0218196723500091

Author

Azeef Muhammed, P. A. ; Volkov, Mikhail V. ; Auinger, Karl. / Cross-connection structure of locally inverse semigroups. In: International Journal of Algebra and Computation. 2023 ; Vol. 33, No. 01. pp. 123-159.

BibTeX

@article{24ae6079834049c590b15dc2e896b986,
title = "Cross-connection structure of locally inverse semigroups",
abstract = "Locally inverse semigroups are regular semigroups whose idempotents form pseudosemilattices. We characterize the categories that correspond to locally inverse semi groups 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 0-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 0-simple semigroups, we show that cross-connections coincide with structure matrices, thus recovering the Rees Theorem by categorical tools.",
author = "{Azeef Muhammed}, {P. A.} and Volkov, {Mikhail V.} and Karl Auinger",
note = "Mikhail V. Volkov is supported by the Ministry of Science and Higher Educationof the Russian Federation (Ural Mathematical Center Project No. 075-02-2022-877). The authors thank the referee for their very meticulous reading of the paper, generous comments and several excellent suggestions which have helped improvethe readability of the paper.",
year = "2023",
month = feb,
day = "1",
doi = "10.1142/S0218196723500091",
language = "English",
volume = "33",
pages = "123--159",
journal = "International Journal of Algebra and Computation",
issn = "0218-1967",
publisher = "World Scientific Publishing Co.",
number = "01",

}

RIS

TY - JOUR

T1 - Cross-connection structure of locally inverse semigroups

AU - Azeef Muhammed, P. A.

AU - Volkov, Mikhail V.

AU - Auinger, Karl

N1 - Mikhail V. Volkov is supported by the Ministry of Science and Higher Educationof the Russian Federation (Ural Mathematical Center Project No. 075-02-2022-877). The authors thank the referee for their very meticulous reading of the paper, generous comments and several excellent suggestions which have helped improvethe readability of the paper.

PY - 2023/2/1

Y1 - 2023/2/1

N2 - Locally inverse semigroups are regular semigroups whose idempotents form pseudosemilattices. We characterize the categories that correspond to locally inverse semi groups 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 0-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 0-simple semigroups, we show that cross-connections coincide with structure matrices, thus recovering the Rees Theorem by categorical tools.

AB - Locally inverse semigroups are regular semigroups whose idempotents form pseudosemilattices. We characterize the categories that correspond to locally inverse semi groups 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 0-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 0-simple semigroups, we show that cross-connections coincide with structure matrices, thus recovering the Rees Theorem by categorical tools.

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=000895570900003

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85144544350

U2 - 10.1142/S0218196723500091

DO - 10.1142/S0218196723500091

M3 - Article

VL - 33

SP - 123

EP - 159

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 01

ER -

ID: 34654264