arXiv subjects
Publications and source records attributed to Snehinh Sen.
In this paper, we explore semirings in which all congruences are finitely generated. Such semirings are dubbed \textit{Congruence Noetherian}. After developing sufficient background and examples, we focus on the canonical positive models of a real order and show that this obvious choice, though not finitely generated as an $\N$-module, is both Congruence Noetherian and flat over $\N$.
We classify fields having finitely many finite non-commutative (not necessarily central) division algebras over them. In the process, we introduce the notion of anti-closure of a field and also make comments on fields having a linear lattice of finite field extensions over them.
The target of this article is to discuss the concept of \textit{commuting probability} of finite groups which, in short, is a probabilistic measure of how abelian our group is. We shall compute the value of commuting probability for many special classes of non-abelian groups and also establish some local and global bounds. We will conclude with a few topics for further reading.