Congruences in ordered sets and LU compatible equivalences

summary:A concept of equivalence preserving upper and lower bounds in a poset $P$ is introduced. If $P$ is a lattice, this concept coincides with the notion of lattice congruence

A remark on spaces over a special local ring

summary:This paper deals with A-spaces in the sense of McDonald over linear algebras A of a certain type. Necessary and sufficient conditions for a submodule to be an A-space are derived

Inertial law of quadratic forms on modules over plural algebra

summary:Quadratic forms on a free finite-dimensional module are investigated. It is shown that the inertial law can be suitably generalized provided the vector space is replaced by a free finite-dimensional module over a certain linear algebra over $\R$ ( real plural algebra) introduced in [1]

Geometry of Cyclic and Anticylic Algebras

summary:The article deals with spaces the geometry of which is defined by cyclic and anticyclic algebras. Arbitrary multiplicative function is taken as a fundamental form. Motions are given as linear transformation preserving given multiplicative function

Inertial law of symplectic forms on modules over plural algebra

summary:In this paper the problem of construction of the canonical matrix belonging to symplectic forms on a module over the so called plural algebra (introduced in [5]) is solved