Presentations for rook partition monoids and algebras and their singular ideals

James East

doi:10.1016/j.jpaa.2018.05.016

Presentations for rook partition monoids and algebras and their singular ideals

James East

Western Sydney University

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

Abstract

We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our presentations use such minimal-size generating sets), and show that the singular part of the rook partition monoid is generated by its idempotents.

Original language	English
Pages (from-to)	1097-1122
Number of pages	26
Journal	Journal of Pure and Applied Algebra
Volume	223
Issue number	3
DOIs	https://doi.org/10.1016/j.jpaa.2018.05.016
Publication status	Published - 2019

Keywords

algebra
monoids
partitions (mathematics)
set theory

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10.1016/j.jpaa.2018.05.016

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title = "Presentations for rook partition monoids and algebras and their singular ideals",

abstract = "We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our presentations use such minimal-size generating sets), and show that the singular part of the rook partition monoid is generated by its idempotents.",

keywords = "algebra, monoids, partitions (mathematics), set theory",

author = "James East",

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PY - 2019

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N2 - We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our presentations use such minimal-size generating sets), and show that the singular part of the rook partition monoid is generated by its idempotents.

AB - We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our presentations use such minimal-size generating sets), and show that the singular part of the rook partition monoid is generated by its idempotents.

KW - algebra

KW - monoids

KW - partitions (mathematics)

KW - set theory

UR - http://handle.westernsydney.edu.au:8081/1959.7/uws:49252

U2 - 10.1016/j.jpaa.2018.05.016

DO - 10.1016/j.jpaa.2018.05.016

M3 - Article

SN - 0022-4049

VL - 223

SP - 1097

EP - 1122

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -

Presentations for rook partition monoids and algebras and their singular ideals

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Keywords

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