关于半环的2-素数和n-弱2-素数理想的一个注记

Q3 Mathematics

Quasigroups and Related Systems Pub Date : 2023-04-01 DOI:10.56415/qrs.v30.20

Biswaranjan Khanra, M. Mandal, S. Das

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引用次数: 0

摘要

我们引入并研究了交换半环中2-素数和n-弱2-素数（分别为弱2-素数）理想的概念。我们证明了积分半域S是一个赋值半环，当且仅当S的每个适当理想都是2-素数，并且在主理想半域中，初理想、拟初理想和2-素数理想的概念是一致的。我们刻画了2-素数理想为素数的半环，也刻画了每个适当理想为n-弱2-素数（分别为弱2-素数）的半环

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A note on 2-prime and n-weakly 2-prime ideals of semirings

We introduce and study the concepts of 2-prime and n-weakly 2-prime (resp. weakly 2-prime) ideals in a commutative semiring. We prove that an integral semidomain S is a valuation semiring if and only if every proper ideal of S is 2-prime and in a principal ideal semidomain the concepts of primary, quasi-primary and 2-prime ideals coincide. We characterize semirings where 2-prime ideals are prime and also characterize semirings where every proper ideal is n-weakly 2-prime (resp. weakly 2-prime)

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来源期刊

Quasigroups and Related Systems Mathematics-Discrete Mathematics and Combinatorics

CiteScore

0.70

自引率

0.00%

发文量