The Stone spectrum of a von Neumann algebra is a generalization of the Gelfand spectrum, as was shown by de Groote. In this article we clarify the structure of the Stone spectra of von Neumann algebras of type In.

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

This two-group, pretest-posttest, quasi-experimental study compared secondary students’ learning of Algebra II materials over a 4-week period when identical instruction by the same teacher was delivered through either embedded blended learning (treatment group; n = 32) or a live-lecture classroom (control group; n = 24). For both groups, instruction was delivered in a normal classroom setting. ...

It is well known that free Boolean algebra on n generators isomorphic to the of functions variables. The distributive lattice monotone In this paper we introduce concept De Morgan function and prove Keywords: Antichain, function, algebra.

We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x∨¬¬x = 1, preserves filtering (or directed) unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To pr...

In this paper, it is shown that the category of stratified $L$-generalized convergence spaces is monoidal closed if the underlying truth-value table $L$ is a complete residuated lattice. In particular, if the underlying truth-value table $L$ is a complete Heyting Algebra, the Cartesian closedness of the category is recaptured by our result.

We investigate the class SRaCAn for 4 n < ! and survey some recent results. We see that RAn | the subalgebras of relation algebras with relational bases | is too weak, and that the class of relation algebras whose canonical extension has an n-dimensional cylindric basis is too strong to deene the class. We introduce the notion of an n-dimensional hyperbasis and show that for any relation algebr...

The theory of elementary toposes plays the fundamental role in the categorial analysis of the intuitionistic logic. The main theorem of this theory uses the fact that sets E(A,Ω) (for any object A of a topos E) are Heyting algebras with operations defined in categorial terms. More exactly, subobject classifier true: 1 → Ω permits us define truth-morphism on Ω and operations in E(A,Ω) are define...

It is well-known that congruences on a Heyting algebra are in one-to-one correspondence with filters of the underlying lattice. If an algebra A has a Heyting algebra reduct, it is of natural interest to characterise which filters correspond to congruences on A. Such a characterisation was given by Hasimoto [1]. When the filters can be sufficiently described by a single unary term, many useful p...

In this note we characterize all subalgebras and homomorphic images of the free cyclic Heyting algebra, also known as the RiegerNishimura lattice N . Consequently, we prove that every subalgebra of N is projective, that a finite Heyting algebra is a subalgebra of N iff it is projective, and characterize projective homomorphic images of N . The atoms and co-atoms of the lattice of all subalgebra...