The aim of this article is to obtain more general forms than the papers of Jun et al. 2010 ; Jun et al. in press . The notions of N-subalgebras of types ∈, qk , ∈,∈ ∨qk , and q,∈ ∨qk are introduced, and the concepts of qk-support and ∈ ∨qk-support are also introduced. Several related properties are investigated. Characterizations of N-subalgebra of type ∈,∈ ∨qk are discussed, and conditions for...

The dynamical quantum Zeno effect is studied in the context of von Neumann algebras. We identify a localized subalgebra on which the Zeno dynamics acts by automorphisms. The Zeno dynamics coincides with the modular dynamics of that subalgebra, if an additional assumption is satisfied. This relates the modular operator of that subalgebra to the modular operator of the original algebra by a varia...

In [14] we showed that for each locally finite unary (total) algebra of finite type, its weak subalgebra lattice uniquely determines its (strong) subalgebra lattice. Now we generalize this fact to algebras having also finitely many binary operations (for example, groupoids, semigroups, semilattices). More precisely, we generalize some ideas from [14] to prove: Let A be a locally finite (total) ...

We prove that the problems of classifying triples of symmetric or skew-symmetric matrices up to congruence, local commutative associative algebras with zero cube radical and square radical of dimension 3, and Lie algebras with central commutator subalgebra of dimension 3 are hopeless since each of them reduces to the problem of classifying pairs of n-by-n matrices up to simultaneous similarity....

It is proved that the following conditions are equivalent: (a) there exists a complete, atomless, σ–centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra, (b) there exists a nowhere dense ultrafilter on ω. Therefore the existence of such algebras is undecidable in ZFC. In ”forcing language” condition (a) says that there exists a non– trivial σ–centered for...

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...