Łukasiewicz环的非交换推广

Q1 Mathematics Journal of Applied Logic Pub Date : 2016-07-01 DOI:10.1016/j.jal.2016.04.001

Albert Kadji , Celestin Lele , Jean B. Nganou

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引用次数: 2

摘要

本文的目的是将Belluce和Di Nola[1]对理想构成mv代数的交换环的研究推广到非交换环。我们研究了理想构成伪mv代数的所有环，这里称之为广义Łukasiewicz环。我们得到了它们(在同构范围内)正是酉特殊原环的直接和。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A non-commutative generalization of Łukasiewicz rings

The goal of the present article is to extend the study of commutative rings whose ideals form an MV-algebra as carried out by Belluce and Di Nola [1] to non-commutative rings. We study and characterize all rings whose ideals form a pseudo MV-algebra, which shall be called here generalized Łukasiewicz rings. We obtain that these are (up to isomorphism) exactly the direct sums of unitary special primary rings.

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