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.
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.
We prove that a generalized periodic, as well as a generalized Boolean, ring is either commutative or periodic. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which imply the commutativity of a gen
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
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 suc
The problem of imbedding an abstract distributive lattice in a Boolean algebra by an algebraic extension was suggested to the writer by M. H. Stone in 1933. Hausdorfff had already given a solution of this problem for the case where the given distributive lattice was a ring of poi
A potential advantage of using a Boolean-ring formalism for propositional formulæ is the large measure of simplification it facilitates. We propose a combined linear and binomial representation for Boolean ring polynomials, with which one can easily apply Gaussian elimination and