Theorem. A commutative B*-algebra K containing an identity e (with \\k*-k\\ =\\k\\2for all &GP and ||e|| =1) is isomorphic (in a norm and * preserving manner) to an algebra B(X) of all bounded complexvalued functions on an essentially unique set X if and only if: (1) Every nonzero closed ideal of K contains a minimal ideal; (2) The sum of two annulets is an annulet. An annulet is here understoo...

In this paper we consider a free associative algebra on three generators over an arbitrary field K. Given a term ordering on the commutative polynomial ring on three variables over K, we construct uncountably many liftings of this term ordering to a monomial ordering on the free associative algebra. These monomial orderings are total well orderings on the set of monomials, resulting in a set of...

let $r$ be a commutative ring with zero-divisor set $z(r)$. the total graph of $r$, denoted by$t(gamma(r))$, is the simple (undirected) graph with vertex set  $r$ where two distinct vertices areadjacent if their sum lies in $z(r)$.this work considers minimum zero-sum $k$-flows for $t(gamma(r))$.both for $vert rvert$ even and the case when $vert rvert$ is odd and $z(g)$ is an ideal of $r$it is s...

In this article we investigate the universal C∗-algebras associated to certain 1dimensional simplicial flag complexes which describe the noncommutative circle. We denote it by S 1 . We examine the K-theory of this algebra and the subalgebras S nc 1 /Ik, Ik . Where Ik, for each k, is the ideal in S 1 generated by all products of generators hs containing at least k + 1 pairwise different generato...

This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

Hilbert was concerned with fundamental problems of invariant theory: given a linear group, G, acting linearly on the ring of polynomials, S = K[X1, . . . , XN ], we let S be the subring of invariants. Is S nitely generated as an algebra over the eld, K, and if so, what are its generators? Assuming it is nitely generated, that is, that S = K[Y1, . . . , YN ′ ]/I, is it the case that I is nitely ...

Applying the idea of soft set theory to lattice implication algebras, the novel concept of (implicative) filteristic soft lattice implication algebras which related to (implicative) filter(for short, (IF -)F -soft lattice implication algebras) are introduced. Basic properties of (IF -)F -soft lattice implication algebras are derived. Two kinds of fuzzy filters (i.e.(∈,∈ ∨qk)((∈,∈ ∨ qk))-fuzzy (...