Radicals of semigroup rings of commutative semigroups

Kelarev, AV

doi:10.1007/bf02573649

Cited by 6 publications

(2 citation statements)

References 43 publications

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“…Note that, for every finite semigroup S , the radical of each semigroup algebra F [S] has been reduced to the radicals of group algebras of the subgroups of S , see [16]. For background information on the radicals of semigroup rings of commutative semigroups and arbitrary semigroup algebras the reader is referred to [19] and [31], respectively.…”

Section: Preliminariesmentioning

confidence: 99%

An Algorithm for Computing the Minimum Distances of Extensions of BCH Codes Embedded in Semigroup Rings

et al. 2006

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Section: Preliminariesmentioning

confidence: 99%

An Algorithm for Computing the Minimum Distances of Extensions of BCH Codes Embedded in Semigroup Rings

et al. 2006

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“…Как правило, при описании радикала полугрупповых алгебр задача сводится к описанию радикала групповых алгебр для подгрупп дан-ной полугруппы либо к описанию радикала прямых слагаемых (если возможно представление в виде прямой суммы подколец), либо радикал полугрупповой алгебры описывается в терминах полугруппы. Для последнего направления получено исчерпывающее описание радикала Джекобсона для полугрупповых колец коммутативных полугрупп (см., например, обзор [2]). При этом радикал полугруппового кольца описан с помощью сепаративной и p-сепаративной кон-груэнций.…”

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Радикалы Полугрупп И Полугрупповых Алгебр

Сокольский¹,

Sokolsky²

2010

Матем. сб.

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Радикалы полугрупп и полугрупповых алгебр В работе рассмотрены различные нижние радикалы полугрупп и пока-зано, как при помощи этих радикалов можно вычислять первичный ради-кал групповых и полугрупповых алгебр. Найдены условия, при которых первичный радикал групповой алгебры совпадает с идеалом, порожден-ным некоторой конгруэнцией.Библиография: 22 названия.Ключевые слова: групповые алгебры, полугрупповые алгебры, ра-дикалы полугрупп, первичный радикал.

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Rings Which Are Sums of Finite Fields

Kelarev¹

1999

Finite Fields and Their Applications

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We describe all semigroup rings and band-graded rings which are direct sums of finite fields. We show that the class of rings which are direct sums of finite fields is closed for taking sums of two subrings. Academic PressSemigroup rings of arithmetical semigroups have nice applications in analytic number theory (see, for example, [14, Sect. 2.1]). We shall describe all semigroup rings which are direct sums of finite fields (Theorem 3). To this end we consider another important construction (Theorem 2) and establish an interesting ring-theoretic property of the class of rings which are direct sums of finite fields (Theorem 1).The preservation of ring properties by sums of rings has been actively investigated by many authors. Let K be a class of rings, and let a ring R be a sum of its subrings R G , where i"1, 2 , n. Suppose that all the R G are in K. Does it follow that R belongs to K? This question has been considered for several classes K; see [1,2,6,8] for references. We only mention that a longstanding difficult problem in this area has been recently solved in [9] and [12]. Namely, examples of rings which are not nil but are sums of two locally nilpotent subrings were constructed. Taking a homomorphic image of a ring introduced in [9], a simpler version of the example was given in [12]. Moreover, it was shown that there exists a primitive ring which is a sum of two Wedderburn radical subrings, which answered several questions known 89

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Radicals of semigroup rings of commutative semigroups

Cited by 6 publications

References 43 publications

An Algorithm for Computing the Minimum Distances of Extensions of BCH Codes Embedded in Semigroup Rings

An Algorithm for Computing the Minimum Distances of Extensions of BCH Codes Embedded in Semigroup Rings

Радикалы Полугрупп И Полугрупповых Алгебр

Rings Which Are Sums of Finite Fields

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