We introduce the equational notion of a monadic bounded algebra (MBA), intended to capture algebraic properties of bounded quantification. The variety of all MBA’s is shown to be generated by certain algebras of two-valued propositional functions that correspond to models of monadic free logic with an existence predicate. Every MBA is a subdirect product of such functional algebras, a fact that...

We show that for any tolerance R on U , the ordered sets of lower and upper rough approximations determined by R form ortholattices. These ortholattices are completely distributive, thus forming atomistic Boolean lattices, if and only if R is induced by an irredundant covering of U , and in such a case, the atoms of these Boolean lattices are described. We prove that the ordered set RS of rough...

As it is clearly suggested by the title, this note is a continuation of [1]. In the latter paper, the authors start from the famous theorem of N. Jacobson which asserts that every ring satisfying the identity x = x for some n ≥ 1 must be commutative (though Jacobson’s result is more general: the existence of a positive integer n(a) for each a ∈ R such that a = a suffices to conclude that the ri...

We study an extension of MV algebras, called μMV algebras, in which minimal and maximal fixed points are definable. The first result is that μMV algebras are term-wise equivalent to divisible MV∆algebras, i.e. a combination of two known extensions of MV algebras: divisible MV algebras [4] and MV∆algebras [6]. Using methods from the two known extensions we derive a number of results about μMV al...

We give examples of direct products of three hyperbolic groups in which there cannot exist an algorithm to decide which finitely presented subgroups are isomorphic. In [1] Baumslag, Short and the present authors constructed an example of a biautomatic group G in which there is no algorithm that decides isomorphism among the finitely presented subgroups of G. The group G was a direct product of ...

4. Proof of Theorem 2. Harish-Chandra [l] and others have proved that every Lie algebra over a field of characteristic zero has a faithful representation. Consequently by Lemma 4, 8 has a faithful representation x—*Qx whose matrices have elements in an algebraic extension $ of g such that t(QxQv) =0 for all x of 31 and all y of 8. We now apply another form of Cartan's criterion for solvability ...

The concept of subdirect sum matrices (a type with overlapping blocks) was introduced in 1999 and has been broadly studied. In this paper we extend by introducing the weighted sum: a blocks allowing to give different weight overlapped blocks. This naturally arises applications regions such as graphs multilayer networks or iterative methods solve linear systems equations based on We analyze same...