A classification of maximal subsemigroups of finite order-preserving transformation semigroups

Yang, Xiuliang

doi:10.1080/00927870008826910

Cited by 19 publications

(6 citation statements)

References 9 publications

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“…The maximal subsemigroups of the singular ideal of O n were incorrectly described and counted in [46]: the given formula for the number of maximal subsemigroups of the singular ideal of O n is correct for 2 ≤ n ≤ 5, but gives only a lower bound when n ≥ 6. A correct description, although no number, was subsequently given in [11].…”

Section: O N and Od Nmentioning

confidence: 99%

Maximal subsemigroups of finite transformation and diagram monoids

et al. 2018

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We describe and count the maximal subsemigroups of many well-known monoids of transformations and monoids of partitions. More precisely, we find the maximal subsemigroups of the full spectrum of monoids of order-or orientationpreserving transformations and partial permutations considered by V. H. Fernandes and co-authors (12 monoids in total); the partition, Brauer, Jones, and Motzkin monoids; and certain further monoids.Although descriptions of the maximal subsemigroups of some of the aforementioned classes of monoids appear in the literature, we present a unified framework for determining these maximal subsemigroups. This approach is based on a specialised version of an algorithm for determining the maximal subsemigroups of any finite semigroup, developed by the third and fourth authors. This allows us to concisely present the descriptions of the maximal subsemigroups, and to more clearly see their common features.

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Section: O N and Od Nmentioning

confidence: 99%

Maximal subsemigroups of finite transformation and diagram monoids

et al. 2018

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“…In this section, we give a complete classification of the maximal subsemigroups of the semigroup M n of all monotone transformations. Here, we can use the classification of the maximal subsemigroups of O n given by Yang Xiuliang ( [10]).…”

Section: The Maximal Subsemigroups Of the Semigroup M Nmentioning

confidence: 99%

“…2) The semigroup S can be only one of the semigroups given in [10], i.e., S =Î n−2 ∪ U for some U ⊆Ĵ n−1 . Hence S is maximal by Lemma 7.…”

Section: From the Condition γ Imentioning

confidence: 99%

“…The semigroup O n of all isotone transformations on the finite chain X n is also of great interest. Yang Xiuliang [10] obtained a complete classification of the maximal subsemigroups of the semigroup O n . Yang Xiuliang and Lu Chunghan [11] received the maximal idempotent-generated and regular subsemigroups of the semigroup O n and etc.…”

Section: Introductionmentioning

confidence: 99%

“…α ∈ (M n \ S) ∩J n−1 . Since S is a maximal subsemigroup of the semigroup O n by the results of Yang Xiuliang ([10]) each L -and each R -class of S contains an idempotent. Therefore, either L α or R α contains an idempotent ε ∈ S.…”

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On the maximal subsemigroups of the semigroup of all monotone transformations

Gyudzhenov

Dimitrova

2006

Discuss. Math. - General Algebra and Applications

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In this paper we consider the semigroup M n of all monotone transformations on the chain X n under the operation of composition of transformations. First we give a presentation of the semigroup M n and some propositions connected with its structure. Also, we give a description and some properties of the classJ n−1 of all monotone transformations with rank n − 1. After that we characterize the maximal subsemigroups of the semigroup M n and the subsemigroups of M n which are maximal inJ n−1 .

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Classical Finite Transformation Semigroups

Ganyushkin¹,

Mazorchuk²

2009

Algebra and Applications

210

199

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Algebra and Applications aims to publish well written and carefully refereed monographs with up-to-date information about progress in all fields of algebra, its classical impact on commutative and noncommutative algebraic and differential geometry, K-theory and algebraic topology, as well as applications in related domains, such as number theory, homotopy and (co)homology theory, physics and discrete mathematics. Particular emphasis will be put on state-of-the-art topics such as rings of differential operators, Lie algebras and super-algebras, group rings and algebras, C*algebras, Kac-Moody theory, arithmetic algebraic geometry, Hopf algebras and quantum groups, as well as their applications. In addition, Algebra and Applications will also publish monographs dedicated to computational aspects of these topics as well as algebraic and geometric methods in computer science. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made.Printed on acid-free paper Springer Science+Business Media springer.com PrefaceSemigroup theory is a relatively young part of mathematics. As a separate direction of algebra with its own objects, formulations of problems, and methods of investigations, semigroup theory was formed about 60 years ago.One of the main motivations for the existence of some mathematical theories are interesting and natural examples. For semigroup theory the obvious candidates for such examples are transformation semigroups. Various transformations of different sets appear everywhere in mathematics all the time. As the usual composition of transformations is associative, each set of transformations, closed with respect to the composition, forms a semigroup.Among all transformation semigroups one can distinguish three classical series of semigroups: the full symmetric semigroup T (M ) of all transformations of the set M ; the symmetric inverse semigroup IS(M ) of all partial (that is, not necessarily everywhere defined) injective transformations of M ; and, finally, the semigroup PT (M ) of all partial transformations of M . If M = {1, 2, . . . , n}, then the above semigroups are usually denoted by T n...

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A classification of maximal subsemigroups of finite order-preserving transformation semigroups

Cited by 19 publications

References 9 publications

Maximal subsemigroups of finite transformation and diagram monoids

Maximal subsemigroups of finite transformation and diagram monoids

On the maximal subsemigroups of the semigroup of all monotone transformations

Classical Finite Transformation Semigroups

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