陈晔, 李勇华. 加法$\mathcal {P}$-正则半环上的$\mathcal {P}$-核正规系[J]. 华南师范大学学报(自然科学版), 2011, (4).
引用本文: 陈晔, 李勇华. 加法$\mathcal {P}$-正则半环上的$\mathcal {P}$-核正规系[J]. 华南师范大学学报(自然科学版), 2011, (4).
$\mathcal {P}$-kernel normal system of an additive $\mathcal {P}$-regular semiring[J]. Journal of South China Normal University (Natural Science Edition), 2011, (4).
Citation: $\mathcal {P}$-kernel normal system of an additive $\mathcal {P}$-regular semiring[J]. Journal of South China Normal University (Natural Science Edition), 2011, (4).

加法\mathcal P-正则半环上的\mathcal P-核正规系

\mathcal P-kernel normal system of an additive \mathcal P-regular semiring

  • 摘要: \mathcalP-正则半群是一类重要的半群,Sen用核正规系的方法描述了\mathcalP-正则半群上的同余. 本文考虑加法\mathcalP-正则半环,在该类半环上引入了\mathcal P-核正规系,证明了该类半环上的每个同余都可以获得一个\mathcalP-核正规系,并且\mathcal P-核正规系惟一地确定了一个同余. 最后对\overset+ C-集是半理想的加法\mathcal P-正则半环刻画了\mathcal P-核正规系.

     

    Abstract: \mathcal P-regular semigroups are an important class of semigroups. Sen described the congruence on a \mathcal P-regular semigroup by means of a \mathcal P-kernel normal system. In this paper we consider the additive \mathcal P-regular semiring and discuss the \mathcal P-kernel normal system of the additive \mathcal P-regular semiring. We prove that every congruence on this kind of semiring can induce a \mathcal P-kernel normal system, and every \mathcal P-kernel normal system uniquely determines a congruence. In the end we illustrate a \mathcal P-kernel normal system of an additive \mathcal P-regular semiring whose \overset+C-set is a semi-ideal.

     

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