A Characterization of Function Rings with Boolean Domain
نویسندگان
چکیده
منابع مشابه
Omega-almost Boolean rings
In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.
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A Boolean ring satisfies the identity x2 = x which, of course, implies the identity x2y − xy2 = 0. With this as motivation, we define a subBoolean ring to be a ring R which satisfies the condition that x2y−xy2 is nilpotent for certain elements x, y of R. We consider some conditions which imply that the subBoolean ring R is commutative or has a nil commutator ideal. Mathematics Subject Classific...
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in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.
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We introduce the family of R-based proto-Boolean rings associated with an arbitrary commutative ring R. They generalize the protoBoolean algebra devised by Brown [4] as a tool for expressing in modern language Boole’s research in The Laws of Thought. In fact the algebraic results from [4] are recaptured within the framework of proto-Boolean rings, along with other theorems. The free Boolean alg...
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Let $R$ be a commutative ring and $I$ an ideal of $R$. The zero-divisor graph of $R$ with respect to $I$, denoted by $Gamma_I(R)$, is the simple graph whose vertex set is ${x in Rsetminus I mid xy in I$, for some $y in Rsetminus I}$, with two distinct vertices $x$ and $y$ are adjacent if and only if $xy in I$. In this paper, we state a relation between zero-divisor graph of $R$ with respec...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1994
ISSN: 0002-9939
DOI: 10.2307/2160359