Normal categories from completely simple semigroups

P. A. Azeef Muhammed

doi:10.1007/978-981-10-1651-6_25

Normal categories from completely simple semigroups

P. A. Azeef Muhammed

University of Kerala

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

1 Citation (Scopus)

Abstract

In this paper, we characterize the normal categories associated with a completely simple semigroup S = M[G; I, Λ; P] and show that the semigroup of normal cones Tℒ(S) is isomorphic to the semi-direct product G^Λ ⋉ Λ. We characterize the principal cones in this category and the Green’s relations in Tℒ(S).

Original language	English
Title of host publication	Algebra and its Applications - ICAA 2014
Editors	Syed Tariq Rizvi, Vincenzo De Filippis, Vincenzo De Filippis, Asma Ali, Asma Ali, Syed Tariq Rizvi, Syed Tariq Rizvi, Asma Ali, Vincenzo De Filippis
Publisher	Springer New York LLC
Pages	387-396
Number of pages	10
ISBN (Print)	9789811016509, 9789811016509, 9789811016509
DOIs	https://doi.org/10.1007/978-981-10-1651-6_25
Publication status	Published - 2016
Externally published	Yes
Event	International Conference on Algebra and its Applications, ICAA 2014 - Aligarh, India Duration: 15 Dec 2014 → 17 Dec 2014

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	174
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Algebra and its Applications, ICAA 2014
Country/Territory	India
City	Aligarh
Period	15/12/14 → 17/12/14

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media Singapore 2016.

Keywords

Completely simple semigroup
Cross-connections
Normal category
Normal cones

Access to Document

10.1007/978-981-10-1651-6_25

Cite this

Azeef Muhammed, P. A. (2016). Normal categories from completely simple semigroups. In S. T. Rizvi, V. De Filippis, V. De Filippis, A. Ali, A. Ali, S. T. Rizvi, S. T. Rizvi, A. Ali, & V. De Filippis (Eds.), Algebra and its Applications - ICAA 2014 (pp. 387-396). (Springer Proceedings in Mathematics and Statistics; Vol. 174). Springer New York LLC. https://doi.org/10.1007/978-981-10-1651-6_25

Azeef Muhammed, P. A. / Normal categories from completely simple semigroups. Algebra and its Applications - ICAA 2014. editor / Syed Tariq Rizvi ; Vincenzo De Filippis ; Vincenzo De Filippis ; Asma Ali ; Asma Ali ; Syed Tariq Rizvi ; Syed Tariq Rizvi ; Asma Ali ; Vincenzo De Filippis. Springer New York LLC, 2016. pp. 387-396 (Springer Proceedings in Mathematics and Statistics).

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title = "Normal categories from completely simple semigroups",

abstract = "In this paper, we characterize the normal categories associated with a completely simple semigroup S = M[G; I, Λ; P] and show that the semigroup of normal cones Tℒ(S) is isomorphic to the semi-direct product GΛ ⋉ Λ. We characterize the principal cones in this category and the Green{\textquoteright}s relations in Tℒ(S).",

keywords = "Completely simple semigroup, Cross-connections, Normal category, Normal cones",

author = "{Azeef Muhammed}, {P. A.}",

note = "Publisher Copyright: {\textcopyright} Springer Science+Business Media Singapore 2016.; International Conference on Algebra and its Applications, ICAA 2014 ; Conference date: 15-12-2014 Through 17-12-2014",

year = "2016",

doi = "10.1007/978-981-10-1651-6_25",

language = "English",

isbn = "9789811016509",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "387--396",

editor = "Rizvi, {Syed Tariq} and {De Filippis}, Vincenzo and {De Filippis}, Vincenzo and Asma Ali and Asma Ali and Rizvi, {Syed Tariq} and Rizvi, {Syed Tariq} and Asma Ali and {De Filippis}, Vincenzo",

booktitle = "Algebra and its Applications - ICAA 2014",

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Azeef Muhammed, PA 2016, Normal categories from completely simple semigroups. in ST Rizvi, V De Filippis, V De Filippis, A Ali, A Ali, ST Rizvi, ST Rizvi, A Ali & V De Filippis (eds), Algebra and its Applications - ICAA 2014. Springer Proceedings in Mathematics and Statistics, vol. 174, Springer New York LLC, pp. 387-396, International Conference on Algebra and its Applications, ICAA 2014, Aligarh, India, 15/12/14. https://doi.org/10.1007/978-981-10-1651-6_25

Normal categories from completely simple semigroups. / Azeef Muhammed, P. A.
Algebra and its Applications - ICAA 2014. ed. / Syed Tariq Rizvi; Vincenzo De Filippis; Vincenzo De Filippis; Asma Ali; Asma Ali; Syed Tariq Rizvi; Syed Tariq Rizvi; Asma Ali; Vincenzo De Filippis. Springer New York LLC, 2016. p. 387-396 (Springer Proceedings in Mathematics and Statistics; Vol. 174).

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

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AB - In this paper, we characterize the normal categories associated with a completely simple semigroup S = M[G; I, Λ; P] and show that the semigroup of normal cones Tℒ(S) is isomorphic to the semi-direct product GΛ ⋉ Λ. We characterize the principal cones in this category and the Green’s relations in Tℒ(S).

KW - Completely simple semigroup

KW - Cross-connections

KW - Normal category

KW - Normal cones

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T3 - Springer Proceedings in Mathematics and Statistics

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A2 - Rizvi, Syed Tariq

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A2 - Ali, Asma

A2 - Rizvi, Syed Tariq

A2 - Ali, Asma

A2 - De Filippis, Vincenzo

PB - Springer New York LLC

T2 - International Conference on Algebra and its Applications, ICAA 2014

Y2 - 15 December 2014 through 17 December 2014

ER -

Normal categories from completely simple semigroups

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