Moroccan Journal of Algebra and Geometry with Applications

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Note on UN-rings

Abdeslam Mimouni 
Department of Mathematics, KFUPM, Dhahran 31261, KSA

Pages 143-153 | Received 10 February 2023, Accepted 07 April 2023, Published 16 June 2023

Abstract

Let R be an associative ring with identity. Then R is said to be a UN-ring if every nonunit element of R can be written as a product of a unit and nilpotent elements. If in every UN-decomposition, the unit and nilpotent commute, the ring R is said to be a strongly UN-ring. In this paper, we study the notions of UN-rings in different contexts of commutative rings such us pullbacks, trivial ring extensions and amalgamations of algebras along ideals. Our aim is to generate new families of UN-rings. Namely, constructing UN-rings issued from pullbacks where the starting rings are not necessarily UN-ring and also to enrich the literature with such a rings. Examples illustrating the aims and scopes of our results are given.

Keywords:  UN-ring, strongly UN-ring, pullbacks, trivial ring extension, amalgamation.

MSC numbers: 13A15, 13A18, 13F05, 13G05, 13C20.

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