For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

In this paper by considering the notion of BCK-module X, we introduce new concept which is named extended BCK-module or briefly X-module and we obtain some interesting results by it. Furthermore, we define the notion of multiplication X-module. 2000 Mathematics subject classification: 06D99 • 08A30

We derive a new four-dimensional partial differential equation with the isospectral Lax representation by shrinking symmetry algebra of reduced quasi-classical self-dual Yang–Mills and applying technique twisted extensions to obtained Lie algebra. Then we find recursion operator for symmetries construct Bäcklund transformation between this Martínez Alonso–Shabat equation. Finally, integrable hi...

Molodtsov [8] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCK-algebras. The notions of positive implicative soft ideals and positive implicative idealistic soft BCK-algebras are intro...

Given a hypergraph G, we introduce a Grassmann algebra over the vertex set, and show that a class of Grassmann integrals permits an expansion in terms of spanning hyperforests. Special cases provide the generating functions for rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All these results are generalizations of Kirchhoff’s matrix-tree theorem. Furthermore, we show tha...

This paper reviews the coverage of formal Relational Algebra as it applies to distributed, federated databases in varying network topologies. The review shows that a number of Relational Algebra extensions allow distributed relations and federation of heterogeneous database schema. More concrete physical Relational Algebra extensions support access plans for multi-database query processing but ...

This paper reviews the coverage of formal Relational Algebra as it applies to distributed, federated databases in varying network topologies. The review shows that a number of Relational Algebra extensions allow distributed relations and federation of heterogeneous database schema. More concrete physical Relational Algebra extensions support access plans for multi-database query processing but ...