If a graded Lie algebra is the direct sum of two graded sub Lie algebras, its bracket can be written in a form that mimics a ”double sided semidirect product”. It is called the knit product of the two subalgebras then. The integrated version of this is called a knit product of groups — it coincides with the ZappaSzép product. The behavior of homomorphisms with respect to knit products is invest...

In their paper [1], H. Ananthnarayan, L. Avramov, and W.F. Moore introduced a connected sum construction for local Gorenstein rings A,B over ring T, which, in the graded Artinian case, can be viewed as an algebraic analogue of topological same name. We give two alternative descriptions this sum: first uses analogues Thom classes vector bundles Gysin homomorphisms, second is terms Macaulay dual ...

Abstract For given Boolean algebras $\mathbb {A}$ and {B}$ we endow the space $\mathcal {H}(\mathbb {A},\mathbb {B})$ of all homomorphisms from to with various topologies study convergence properties sequences in . We are particular interested situation when is a measure algebra as this case obtain natural tool for studying topological ultrafilters on random extensions set-theoretical universe....

A universal algebra is simple if and only if it has more than one element and there are no proper homomorphisms defined upon it. In this note we study a related notion : an algebra is pseudo-simple if and only if it has more than one element and is isomorphic to all its proper (i.e., non-one-element) homomorphic images. The two concepts simplicity and pseudo-simplicity are examples of concepts ...

The concept of a Hopf algebra originated in topology. Classically, Hopf algebras are defined on the basis of unital modules over commutative, unital rings. The intention of the present work is to study Hopf algebra formalism (§1.2) from a universal-algebraic point of view, within the context of entropic varieties. In an entropic variety, the operations of each algebra are homomorphisms, and ten...

We consider Fréchet algebras which are subalgebras of the algebra F = C [[X]] of formal power series in one variable and of Fn = C [[X1, . . . , Xn]] of formal power series in n variables where n ∈ N. In each case, these algebras are taken with the topology of coordinatewise convergence. We begin with some basic definitions about Fréchet algebras, (F )-algebras, and other topological algebras, ...

Algebraic systems with partial operations have different ways to interpret equality between two terms of the language. A strong identity is a formula which says that two terms are equal in the algebra if the existence of one of them implies the existence of the other one and in the case of existence their values are equal. A class of partial algebras defined by a set of strong identities is cal...

In this paper, we further develop the study of rings integro-differential-delay operators considered as noncommutative polynomial algebras satisfying standard calculus identities. Within algebraic analysis approach, show that transformations and reductions linear differential time-delay systems can be interpreted homomorphisms isomorphisms finitely presented left modules over an algebra operato...