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Malik Tusif Ahmed

Publications and source records attributed to Malik Tusif Ahmed.

5 recordsLinked to original sources
arXiv2026

Commutative rings with square-difference factor absorbing factorization

We introduce and study sdf-absorbing factorization rings (SAF-rings), in which every regular ideal is a finite product of square-difference factor absorbing ideals. We investigate their behavior under direct products, localizations, factor rings, and module idealizations, and establish connections with SP-rings, Dedekind rings, and N-rings. We also introduce strongly sdf-absorbing factorization rings (SSAF-rings), relate them to SSP-rings and almost multiplication rings, and prove that the Noetherian SSAF-rings are precisely the ZPI-rings. Applications to module idealizations and monoid rings are also presented.

math.AC↗
arXiv2020

Commutative rings with invertible-radical factorization

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties under homomorphic image and their transfer to various contexts of constructions such as direct product, trivial ring extension and amalgamated duplication of a ring along an ideal. Our results generate examples that enrich the current literature with new and original families of rings satisfying these properties.

math.AC↗
arXiv2017

Commutative Rings with Two-Absorbing Factorization

We use the concept of 2-absorbing ideal introduced by Badawi to study those commutative rings in which every proper ideal is a product of 2-absorbing ideals (we call them TAF-rings). Any TAF-ring has dimension at most one and the local TAF-domains are the atomic pseudo-valuation domains.

math.AC↗
arXiv2016

SP-rings with zero-divisors

We characterize the commutative rings whose ideals (resp. regular ideals) are products of radical ideals.

math.AC↗