Invertible Rings and Axiomatic Algebra

Some properties of Invertible Elements in Fuzzy Banach algebras

In this paper, we introduce fuzzy Banach algebra and study the properties of invertible elements and its relation with opensets. We obtain some interesting results.

Invertible Algebras with an augmentation map

We briefly survey results about Invertible Algebras (algebras having bases that consist entirely of units) and other related notions. In addition, we consider the existence of an augmentation map as a possible way in which results about group rings, the archetypical invertible algebras, may be extended to more general settings. 1 Invertible Algebras and Some Related Notions Section 1 of this pa...

On the denseness of the invertible group in uniform Frechet algebras

A note on uniquely (nil) clean ring

A ring R is uniquely (nil) clean in case for any $a in R$ there exists a uniquely idempotent $ein R$ such that $a-e$ is invertible (nilpotent). Let $C =(A V W B)$ be the Morita Context ring. We determine conditions under which the rings $A,B$ are uniquely (nil) clean. Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.

Witt rings of quadratically presentable fields

This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...