ON JACOBSON RADICAL OF A SEMIRING
ON JACOBSON RADICAL OF A SEMIRING
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发表时间：
2005
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通讯作者：
S. Sardar
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作者：
S. Sardar
引入了半环和半单半环的Jacobson根的概念，并利用算子半环刻画了它们。AMS数学学科分类（2000）：16Y60、16Y99、20N10表征。得到了半环S的Jacobson根与S的右算子半环R的Jacobson根之间的关系，并利用它得到了半环的Jacobson根的特征，类似于环论和半环论中的一些结果（5）.然后，借助于半环的次直和的概念，利用“半环S是半单的当且仅当它的右算子半环R是半单的”这一结果，得到了半单半环的若干刻划.关于半环、半环、半环的算子半环和环的范畴，我们参考（4）、（9）、（1）、（6）和其中的参考文献.在本文中，半环被假定为具有零、左单位元、右单位元。还假设S半模是可加可消的。
We introduce the notions of Jacobson radical of a semiring and semisimple semiring and characterize them via operator semirings. AMS Mathematics Subject Classification (2000): 16Y60, 16Y99, 20N10 characterizations. We obtain the relation between the Jacobson radical of a semiring S and that of the right operator semiring R of S, which we use to obtain characterizations of Jacobson radical of a semiring analogous to familiar results of the ring theory and semiring theory, (5). Then, with the help of the notion of subdirect sum of semiring, introduced at the outset in a similar way to that in ring, (6), and using the result that "a semiring S is semisimple if and only if its right operator semi- ring R is semisimple", a number of characterizations of semisimple semiring is obtained. For preliminaries of semirings, semirings, operator semirings of a semi- ring and rings we refer to (4), (9), (1), (6) and references therein. Throughout this paper a semiring is assumed to be with zero, the left unity, the right unity. It is also assumed that a S semimodule is additively cancellative.