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ON S-ARMENDARIZ RINGS

Salah Eddine Mahdou|Mohamed Chhiti
장전수학회 (Jangjeon Mathematical Society)|2024.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제27권 제2호|pp. 145-156|DOI 10.17777/pjms.2024.27.2.005

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참고문헌

키워드

trivial ring extensionS-Armendariz ringamalgamated algebras along an ideal
주제분류수학

초록

In this paper, we introduce a new class of rings called S-Armendariz rings, which is a weak version of Armendariz rings. Any Armendariz ring is naturally an S-Armendariz ring, and when S ⊆ U(R), these two classes coincide. We study the transfer of this notion to various contexts of commutative ring extensions such as direct product, trivial ring extensions and amalgamated algebras along ideals. Our results generate new families of examples of non Armendariz S-Armendariz rings.

Abstract

In this paper, we introduce a new class of rings called S-Armendariz rings, which is a weak version of Armendariz rings. Any Armendariz ring is naturally an S-Armendariz ring, and when S ⊆ U(R), these two classes coincide. We study the transfer of this notion to various contexts of commutative ring extensions such as direct product, trivial ring extensions and amalgamated algebras along ideals. Our results generate new families of examples of non Armendariz S-Armendariz rings.

참고문헌 (41)

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