带吸收因式分解的乘法网格

arXiv - MATH - Commutative Algebra Pub Date : 2024-08-02 DOI:arxiv-2408.01100

Andreas Reinhart, Gulsen Ulucak

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引用次数: 0

摘要

在[22]中，Yassine 等人引入了具有非零标识的互素环中的 1 吸素ideals 概念。本文将研究 C 格中 1-absorbing 素元的概念。我们研究了其中每个元素都是 1-absorbing primeelements 的有限乘积的 C 格（我们简称它们为 OAFLs）。此外，我们还研究了具有 2 吸素因式分解的 C 网格（简称 TAFL）。

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Multiplicative Lattices with Absorbing Factorization

In [22], Yassine et al. introduced the notion of 1-absorbing prime ideals in commutative rings with nonzero identity. In this article, we examine the concept of 1-absorbing prime elements in C-lattices. We investigate the C-lattices in which every element is a finite product of 1-absorbing prime elements (we denote them as OAFLs for short). Moreover, we study C-lattices having 2-absorbing factorization (we denote them as TAFLs for short).

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arXiv - MATH - Commutative Algebra

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