The main result of this paper is a characterization of the strongly algebraically closed algebras in the  lattice of all real-valued continuous functions and the equivalence classes of $\lambda$-measurable. We shall provide conditions  which strongly algebraically closed algebras carry a strictly positive Maharam submeasure. Particularly, it is proved that if $B$ is a strongly algebraically closed lattice  and $(B,\, \sigma)$ is a Hausdorff space  and $B$ satisfies  the   $G_\sigma$ property, then $B$ carries a strictly positive Maharam submeasure.

The aim of this paper is to construct an algebraic hyperstructure over a set G corresponding to a Boolean algebra B and a function S:GB. In order to accomplish this goal we will need to define a hyperoperation on the set G. We define, ab =a^6 b={gEG/s(g)<=s(a)vs(b)} and prove that if the image of G is a v -semilattice or constitute a partition of 1 in B, then (G, ^6) is a hypergroup.

Double Boolean algebras (dBas) are algebraic structures D = (D, u, t,: , ⌟ ,? , >) of type (2, 2, 1, 1, 0, 0), introduced by Rudolf Wille to capture the equational theory of the algebra of protoconcepts. Our goal is an algebraic investigation of dBas, based on similar results on Boolean algebras. In this paper, first we characterize filters on dBas as deductive systems and we give many characterization of primary filters(ideals). Second, for a given dBa, we show that the set of its filters F(D) (resp. ideals I(D)) is endowed with the structure of distributive pseudo-complemented lattices, Heyting algebras and residuated lattices. We finish by introducing the notions of annihilators and co-annihilators on dBas and investigate some relalted properties of them. We show that pseudo-complement of an ideal I (filter F) is the annihilator I∗ of I ( co-annihilator F∗ ) and the set of annihilators (co-annihilators) forms a Boolean algebra.

In this paper, some new properties of EQ-algebras are investigated. We intro-duce and study the notion of Boolean center of lattice ordered EQ-algebras with bottom element. We show that in a good ℓ EQ-algebra E with bottom element the complement of an element is unique. Furthermore, Boolean elements of a good bounded lattice EQ-algebra are characterized. Finally, we obtain conditions under which Boolean center of an EQ-algebra E is the subalgebra of E.

This paper presents a new method for simplification of Boolean functions based on Boolean differences. The proposed method is applicable to various forms of Boolean functions, including truth tables and Binary Decision Diagrams (BDDs). The Boolean differences are extended to cover the truth tables with don't-care components and cutset graphs in BDDs. The results of simplification agree with Quine-McCluskey and ESPRESSO methods. Experimental tests on MCNC and Berkeley PLA benchmarks show that the proposed method gains a performance of 1.5-10 times faster than ESPRESSO. The algorithms of the proposed method are implemented in Java/Perl/C++, and a toolset for logic function simplification is developed.

In this paper, the notion of an M-function and cut function on a set, are in-troduced and investigated several properties. We use algebraic properties to introduce an algorithm which show that every , nite MV-algebras and Fibonacci sequences determines a block-code and presented some connections between Fibonacci sequences, MV-algebras and binary block-codes. Furthermore, an MV-algebra arising from block-codes is established.

Equality algebras were introduced by S. Jenei as a possible algebraic semantic for fuzzy type theory. In this paper, we introduce some types of filters such as (positive) implicative, fantastic, Boolean, and prime filters in equality algebras and we prove some results which determine the relation between these filters. We prove that the quotient equality algebra induced by an implicative filter is a Boolean algebra, by a fantastic filter is a commutative equality algebra, and by a prime filter is a chain, under suitable conditions. Finally, we show that positive implicative, implicative, and Boolean filters are equivalent on bounded commutative equality algebras.

It is shown that every locally idempotent (locally m-pseudoconvex)Hausdorff algebra A with pseudoconvex von Neumann bornology is a regular (respectively, bornological) inductive limit of metrizable locally m-(kB-convex) subalgebras AB of A. In the case where A, in addition, is sequentially BA-Complete (sequentially advertibly Complete), then every subalgebraAB is a locally m-(kB-convex) Frechet algebra (respectively, an advertibly Complete metrizable locally m-(kB-convex) algebra) for some kB Î (0, 1]. Moreover, for a commutative unital locally m-pseudoconvex Hausdorff algebra A over C with pseudoconvex von Neumann bornology, which at the same time is sequentially BA-Complete and advertibly Complete, the statements (a)–(j) of Proposition 3.2 are equivalent.

The Lifting Idempotent Property (LIP) of ideals in commutative rings inspired the study of Boolean lifting properties in the context of other concrete algebraic structures (MV-algebras, commutative ℓ-groups, BL-algebras, bounded distributive lattices, residuated lattices, etc. ), as well as for some types of universal algebras (C. Muresan and the author defined and studied the Congruence Boolean Lifting Property (CBLP) for congruence modular algebras). A lifting ideal of a ring R is an ideal of R fulfilling LIP. In a recent paper, Tarizadeh and Sharma obtained new results on lifting ideals in commutative rings. The aim of this paper is to extend an important part of their results to congruence with CBLP in semidegenerate congruence modular algebras. The reticulation of such algebra will play an important role in our investigations (recall that the reticulation of a congruence modular algebra A is a bounded distributive lattice L(A) whose prime spectrum is homeomorphic with Agliano’ s prime spectrum of A). Almost all results regarding CBLP are obtained in the setting of semidegenerate congruence modular algebras having the property that the reticulations preserve the Boolean center. The paper contains several properties of congruences with CBLP. Among the results we mention a characterization theorem of congruence with CBLP. We achieve various conditions that ensure CBLP. Our results can be applied to a lot of types of concrete structures: commutative rings, ℓ-groups, distributive lattices, MV-algebras, BL-algebras, residuated lattices, etc.