In this paper we study sub-semigroups of a zero-divisor semigroup S determined by properties of the zero-divisor graph Γ(S). We use these sub-semigroups to study the correspondence between zero-divisor semigroups and zero-divisor graphs. We study properties of sub-semigroups of Boolean semigroups via the zero-divisor graph. As an application, we provide a characterization of the graphs which ar...

In this paper, it is shown that the Boolean ring of a commutative isomorphic to clopens its prime spectrum. particular, Stone's Representation Theorem generalized. The spectrum given R identified with Pierce R. discreteness spectra characterized. It also proved space connected components compact X X. As another major result, morphism rings between complete preserves suprema if and only induced ...

It has been proved that almost all n-bit Boolean functions have exact classical query complexity n. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost all n-bit Boolean functions can be computed by an exact quantum algorithm with less than n queries. More exactly, we prove that ANDn is the only n-bit Boolean f...

Model checking is an algorithmic approach for automatically verifying whether a hardware or software system functions correctly. Typically, computation is carried over Boolean algebras using binary decision diagrams (BDDs) or satisfiability (SAT) solvers. In this paper we show that computation for model checking can also be carried over the dual Boolean rings of the Boolean algebras by means of...

This article is devoted to two different generalizations of projective Boolean algebras: openly generated Boolean algebras and tightly σ-filtered Boolean algebras. We show that for every uncountable regular cardinal κ there are 2 pairwise non-isomorphic openly generated Boolean algebras of size κ > א1 provided there is an almost free non-free abelian group of size κ. The openly generated Boolea...