Strongly ϕ-n-irreducible ideals

Darani Ahmad Yousefian; Mahdou Najib; Moussaoui Sanae

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Strongly ϕ-n-irreducible ideals

机译：Strongly ϕ-n-irreducible ideals

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Let R be a commutative ring, I be an ideal of R, n be a non-null positive integer and ϕ:?(R)→?(R)∪{∅} be a function where ?(R) is the set of ideals of R. In this paper, we define a new generalization of strongly n-irreducible ideals called strongly ϕ-n-irreducible ideal, that is, whenever I1∩⋯∩In+1⊆I and I1∩⋯∩In+1⊈ϕ(I) for I1,…,In+1 ideals of R, then there are n of the Ii’s whose intersection is in I. We study the stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal.

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来源
《Journal of algebra and its applications》 |2022年第12期|共12页
作者
Darani Ahmad Yousefian; Mahdou Najib; Moussaoui Sanae;
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作者单位

Department of Mathematics, University of Mohaghegh Ardabili, Ardabil,Iran;

Modelling and Mathematical Structures Laboratory, Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S.M. Ben Abdellah Fez,Morocco;

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正文语种英语
中图分类代数、数论、组合理论;
关键词
Trivial ring extension; amalgamation of ring along an ideal; strongly n-irreducible ideal; strongly ϕ-n-irreducible ideal;

Strongly ϕ-n-irreducible ideals

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