منابع مشابه
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...
متن کاملInference 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...
متن کاملRings 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...
متن کاملInference with Idempotent Valuations
Valuation based systems verifying an idem potent property are studied. A partial or der is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valu ations: as infimum of the most informative valuations or as supremum of the least in formative ones. It is studied how to carry out computations with both representations in ...
متن کاملRings for which every simple module is almost injective
We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1963
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1963-0142596-0