Work

Rings Whose Non-Invertible Elements Are Strongly Nil-Clean

Year: 2024

Type: article

Abstract: We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of a commuting nilpotent and an idempotent. In addition, we examine those rings in which the non-units are uniquely nil-clean in the sense that they are a sum of a nilpotent and an unique idempotent. In fact, we succeeded to prove that these two classes of rings can completely be characterized in terms of already well-studied and fully described sorts of rings.

Source: Lobachevskii Journal of Mathematics

DOI: 10.1134/s1995080224602649

Authors: P. Danchev, O. Hasanzadeh, A. Javan, A. Moussavi

Institutions: Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Tarbiat Modares University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Bulgarian Academy of Sciences, Tarbiat Modares University

OpenAlex ID: W4407932226

FWCI: 2.236

Cites: 28

Cited by: 2

Related to: 10