Alternative rings with idempotent

Idempotent generated algebras and Boolean powers of commutative rings

Boolean powers were introduced by Foster [5]. It was noticed by Jónsson in the review of [6], and further elaborated by Banaschewski and Nelson [1], that the Boolean power of an algebra A by a Boolean algebra B can be described as the algebra of continuous functions from the Stone space of B to A, where A has the discrete topology. It follows that a Boolean power of the group Z is an `-group ge...

Alternative Loop Rings

DRAFT Abstract The right alternative law implies the left alternative law in loop rings of characteristic other than 2. We also exhibit a loop which fails to be a right Bol loop, even though its characteristic 2 loop rings are right alternative.

Inference with Idempotent Valuations

Valuation based systems verifying an idem-potent property are studied. A partial order is deened between the valuations giving them a lattice structure. Then, two diierent strategies are introduced to represent valuations: as innmum of the most informative valuations or as supremum of the least informative ones. It is studied how to carry out computations with both representations in an eecient...

Rings in which elements are the sum of an‎ ‎idempotent and a regular element

Let R be an associative ring with unity. An element a in R is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von Neumann) element in R. If every element of R is r-clean, then R is called an r-clean ring. In this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. Further we prove that if 0 and 1 are the only idempotents...

Some Questions concerning Alternative Rings