Automorphisms of the Endomorphism Semigroup of a Free Inverse Semigroup

Mashevitzky, G.; Schein, Boris M.; Zhitomirski, Grigori

doi:10.1080/00927870600850610

Cited by 25 publications

(23 citation statements)

References 4 publications

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“…All automorphisms of the category Θ 0 are known in the following cases (see [3], [14], [15], [13], [11], [24], [17]) .…”

Section: Aut (θ 0 )mentioning

confidence: 99%

Problems in algebra inspired by universal algebraic geometry

Plotkin

2006

J Math Sci

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Let Θ be a variety of algebras. In every Θ and every algebra H from Θ one can consider algebraic geometry in Θ over H. We consider also a special categorical invariant K Θ (H) of this geometry. The classical algebraic geometry deals with the variety Θ = Com − P of all associative and commutative algebras over the ground field of constants P . An algebra H in this setting is an extension of the ground field P . Geometry in groups is related to varieties Grp and Grp − G, where G is a group of constants. The case Grp − F where F is a free group, is related to Tarski's problems devoted to logic of a free group.The described general insight on algebraic geometry in different varieties of algebras inspires some new problems in algebra and algebraic geometry. The problems of such kind determine, to a great extent, the content of universal algebraic geometry.For example, a general and natural problem is:When do the algebras H 1 and H 2 have the same geometry?or more specifically,What are the conditions on algebras from a given variety Θ which provide coincidence of their algebraic geometries?We consider two variants of coincidence:2) These categories are equivalent. This problem is highly connected with the following general algebraic problem:Let Θ 0 be the category of all free in Θ algebras W = W (X), where X is finite. Consider the groups of automorphisms Aut (Θ 0 )

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“…All automorphisms of the category Θ 0 are known in the following cases (see [3], [14], [15], [13], [11], [24], [17]) .…”

Section: Aut (θ 0 )mentioning

confidence: 99%

Problems in algebra inspired by universal algebraic geometry

Plotkin

2006

J Math Sci

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“…Analogous problems dealing with varieties of semigroups were solved by Mashevitzky and Schein [16] for the variety of all monoids and by Formanek [8] for the variety of all groups. However, we solve the problem not only for the variety of all bands but also for all subvarieties of this variety.…”

Section: Introductionmentioning

confidence: 99%

Automorphisms of Endomorphism Monoids of Relatively Free Bands

Araújo¹,

Konieczny²

2007

Proceedings of the Edinburgh Mathematical Society

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“…For example, Schein [8] proved that if M 1 and M 2 are two partially ordered sets, semilattices, distributive lattices, or Boolean algebras, then End(M 1 ) ª = End(M 2 ) if and only if M 1 and M 2 are isomorphic or anti-isomorphic. For other results of this kind, see [2], [4], and [5].…”

Section: Introductionmentioning

confidence: 99%