Finite algebras with no independent basis of identities

We prove that, for any finite field , there exists a finite linear -algebra with no independent basis for its identities. Received March 17, 1992; accepted in final form February 28, 1997.     

On independent subsets of Boolean algebras

We give here a partial solution to a problem of Monk ([2]). Let κ be a regular cardinal and let {L_i∶i<κ} be a family of linear orderings with first element such that noL _i contains a strictly decreasing sequence of length κ⁺. Then $$Ind\left( {\prod\limits_{i< \kappa } {Intalg(L_i )} } \right) \leqslant 2^\kappa .$$      

VMO spaces not having Schauder basis

ПустьA _n (n=0, 1, 2, ...) — последо вательность δ-алгебр, порождаемых двоичны ми отрезками [k2^?n , (k+1)2^?n ) (0≦k<2 ⁿ ). Замыкание множества двоичных с тупенчатых функций по норме      

Finite arithmetical affine complete algebras having no proper subalgebras

Presented by E. Fried.     

Algebraic and topological closure conditions for classes of pseudo-Boolean functions

We examine classes of real-valued functions of 0-1 variables closed under algebraic operations as well as topological convergence, and having a certain local characteristic (requiring that any function not in the class should have a k-variable minor not belonging to this class). It is shown that for k=2, the only 4 maximal classes with these properties are those of submodular, supermodular, monotone increasing and monotone decreasing functions. All the 13 locally defined closed classes are determined and shown to be intersections of the 4 maximal ones. All maximal classes for k≥3 are determined and characterized by the sign of higher order derivatives of the functions in the class.     

The property of having independent basis in semigroup varieties

There exist independently based semigroup varieties and , , such that has no cover in the interval [ ; ].Translated from Algebra i Logika, Vol. 44, No. 1, pp. 81–96, January–February, 2005.     

Pseudo-trees and Boolean algebras

We consider Boolean algebras constructed from pseudo-trees in various ways and make comments about related classes of Boolean algebras.     

On representation of finite pseudo-Boolean algebras and one of its applications

Translated from Matematicheskie Zametki, Vol. 52, No. 2, pp. 127–137, August, 1992.