Congruences associated with inverse transversals.
A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. The present paper is devoted to the study of completely regular semigroup congruences on bands of π-groups.
We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.
We generalize the correspondence between basic algebras and lattices with section antitone involutions to a more general case where no lattice properties are assumed. These algebras are called conjugated if this correspondence is one-to-one. We get conditions for the conjugary of such algebras and introduce the induced relation. Necessary and sufficient conditions are given to indicated when the induced relation is a quasiorder which has “nice properties", e.g. the unary operations are antitone...
A construction of cell algebras is introduced and some of their properties are investigated. A particular case of this construction for lattices of nets is considered.
By max-plus algebra we mean the set of reals equipped with the operations and for A vector is said to be a generalized eigenvector of max-plus matrices if for some . The investigation of properties of generalized eigenvectors is important for the applications. The values of vector or matrix inputs in practice are usually not exact numbers and they can be rather considered as values in some intervals. In this paper the properties of matrices and vectors with inexact (interval) entries...