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Ganyushkin O., Mazorchuk V. — Classical Finite Transformation Semigroups.

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Название: Classical Finite Transformation Semigroups.

Авторы: Ganyushkin O., Mazorchuk V.

Аннотация:

“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 Tn, ISn and PTn, respectively….
The aim of the present book is to partially fill the gaps in the literature.
In the book we introduce three classical series of semigroups, and for them we describe generating systems, ideals, Green’s relations, various classes of subsemigroups, congruences, conjugations, endomorphisms, presentations, actions on sets, linear representations and cross-sections. Some of the results are very old and classical, some are quite young. In order not to overload the reader with too technical and specialized results, we decided to restrict the area of the present book to the above-mentioned parts of the theory of transformation semigroups.\
The book was thought to be an elementary introduction to the theory of transformation semigroups, with a strong emphasis on the concrete examples in the form of three classical series of finite transformation semigroups, namely, Tn, ISn and PTn.”

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Рубрика: Математика/

Статус предметного указателя: Неизвестно

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Количество страниц: 314

Добавлена в каталог: 29.12.2011

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