arXiv subjects

Vivek Bhabani Lama

Publications and source records attributed to Vivek Bhabani Lama.

4 recordsLinked to original sources

arXiv2026

Invertibility of Anticommutator and Commutators of Higher Degree of $n$-potent Elements

We introduce and study the notion of commutators and anti-commutator of higher degrees for ring elements, which generalize the concept of commutator and anti-commutator of ring elements. In particular, we study the invertibility of the degree $n$ commutators and anticommutator of $n$-potent elements. Under natural conditions on the ring, we relate the invertibility of degree $n$ commutators and anticommutator of $n$-potent elements. We also relate the invertibility of degree $n$ commutators and anticommutator of $n$-potent elements with the invertibililty of higher commutators and anticommutator. Finally, we study ring extensions in which the invertibility of degree $n$ commutators and anticommutator of $n$-potent elements is inherited from its base ring.

math.RA↗

arXiv2026

Licci Property of Complementary Edge Ideals

In this article, we characterize the class of complementary edge ideals which satisfy the licci property in terms of the underlying graph. Using this characterization, we associate the licci property of a complementary edge ideal to its other algebraic properties. Finally, we provide two different probability regimes for which the complementary edge ideals of random graphs are licci with high probability and not licci with high probability respectively.

math.AC↗

arXiv2025

Defect Functions Between Filtrations of Ideals

We introduce and study the defect function associated to a pair of filtrations of ideals, which generalizes the symbolic defect of ideals. Under the assumption that the Rees algebra of one filtration is Noetherian and that a natural graded module measuring the interaction between the filtrations is finitely generated over it, we show that the corresponding defect function is asymptotically a quasi-polynomial. Moreover, the defect function becomes eventually polynomial when the Rees algebra of the first filtration is standard graded. For filtrations arising from saturations and ordinary powers of monomial ideals, we further analyze the structure of the quasi-polynomial. We prove that the top two coefficients of the eventual quasi-polynomial are constant under natural hypotheses.

math.AC↗

arXiv2022

Extensions of I-Reversible Rings

A ring $R$ is said to be i-reversible if for every $a,b$ $\in$ $R$, $ab$ is a non-zero idempotent implies $ba$ is an idempotent. It is known that the rings $M_n(R)$ and $T_n(R)$ (the ring of all upper triangular matrices over $R$) are not i-reversible for $n \geq 3$. In this article, we provide a non-trivial i-reversible subring of $M_n(R)$ when $n \geq 3$ and $R$ has only trivial idempotents. We further provide a maximal i-reversible subring of $T_n(R)$ for each $n\geq 3$, if $R$ is a field. We then give conditions for i-reversibility of Trivial, Dorroh and Nagata extensions. Finally, we give some independent sufficient conditions for i-reversibility of polynomial rings, and more generally, of skew polynomial rings.

math.RA↗