arXiv subjects

Sukhendu Kar

Publications and source records attributed to Sukhendu Kar.

3 recordsLinked to original sources

arXiv2026

On Strongly $m$-$\Delta$-clean ring

Motivated by the recent study of strongly $\Delta$-clean rings, we introduce and study strongly $m$-$\Delta$-clean rings. We establish their fundamental properties and characterize strongly $m$-$\Delta$-clean rings via lifting $m$-potent elements modulo $\Delta(R)$. We prove that every $m$-$\Delta$-clean ring is clean and that the factor ring of a strongly $m$-$\Delta$-clean ring modulo its Jacobson radical is reduced. Finally, we investigate corner rings, Morita context rings, and the relationships of these rings with $\Delta$-clean, local, semipotent, and strongly $m$-nil clean rings.

math.RA↗

arXiv2026

On Quasi-Nil Clean Rings

In this paper, we introduce a new type of ring, called quasi-nil clean ring, where each element of the ring is the sum of a quasi-idempotent and a nilpotent element. We also investigate a particular class of ring, called strongly quasi-nil clean ring whose each element is the sum of a quasi-idempotent and a nilpotent element, where they commute. Our primary objective is to study the structural properties of these new class of rings, explore their relationships with existing classes of rings and establish some key characterizations. In the commutative setting, we provide a complete characterization in terms of quasi-Boolean quotients. Moreover we discuss about quasi-cleanness of amalgamated algebra and group ring.

math.RA↗

arXiv2026

Graded m-nil clean ring

In this paper, we introduce the concept of graded m-nil clean ring to extend the existing notion of graded nil-clean ring introduced in [10]. We explore fundamental properties of these rings, emphasizing the interplay between the identity component and the graded structure. We investigate certain conditions under which graded group rings, graded matrix rings and graded amalgamated algebras inherit the m-nil clean property from their components. Specifically, we establish sufficient conditions for graded group rings and graded matrix rings over commutative m-nil clean rings to be graded m-nil clean rings.

math.RA↗