Characterizing f-rings

Generalized f-clean rings

In this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. Next, we investigate some properties of such rings. We prove that $M_n(R)$ is n-f-clean for any n-f-clean ring R. We also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

Characterizing Quaternion Rings

We consider the problem of classifying noncommutative R-algebras of low rank over an arbitrary base ring R. We unify and generalize the many definitions of quaternion ring, and give several necessary and sufficient conditions which characterize them. Let R be a commutative, connected Noetherian ring (with 1). Let B be an algebra over R, an associative ring with 1 equipped with an embedding R →֒ ...

Characterizing Reduced Witt Rings Ii

generalized f-clean rings

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

Characterizing Quaternion Rings over an Arbitrary Base

We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra. A quaternion algebra is a central simple algebra of dimension 4 over a field F . Generalizations of the notion of quaternion algebra to other commutative base rings R...