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.
متن کاملSingle Axioms for Boolean Algebra
Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction technique...
متن کاملPostulate-sets for Boolean Rings
1. Introduction. Boolean rings (or generalized Boolean algebras), defined by Stone, are rings in which every element is idempotent. Sets of postulates for these rings have been given by Stone(2) and by Stabler(8). I give in this paper a number of additional postulate-sets for such rings. The sets are all expressed in terms of ring addition and multiplication. Stone's postulates for Boolean ring...
متن کاملomega-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.
متن کاملProto-Boolean rings
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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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1970
ISSN: 0386-2194
DOI: 10.3792/pja/1195520453