Let A be a Banach algebra with a Hilbert space norm (norm defined by a scalar product). We shall call A a right complemented algebra if it has the property that the orthogonal complement of a right ideal is again a right ideal. This notion was introduced in the author's doctoral thesis [5]. It was proved that under certain additional assumptions every right complemented algebra is left compleme...

Commutative H∗-algebra is characterized in terms of the property that the orthogonal complement of a right ideal is a left ideal.

A ring R is called a left APP-ring if the left annihilator lR(Ra) is right s-unital as an ideal of R for any element a ∈ R. We consider left APP-property of the skew formal power series ring R[[x;α]] where α is a ring automorphism of R. It is shown that if R is a ring satisfying descending chain condition on right annihilators then R[[x;α]] is left APP if and only if for any sequence (b0, b1, ....

background: one of the important etiologies for cryptogenic stroke is paradoxical embolization secondary to patent foramen ovale (pfo). foramen ovale can secondarily reopen due to pulmonary arterial hypertension (pah) which is common among the older age. pah is known as a frequent and life threatening complication of copd. the aim of this study was to determine the prevalence of pfo between cop...

The purpose of this paper is to study matrix hemiring $S_{2}$ via fuzzy subsets and fuzzy $h$-ideals.

Introduction : Previous researches showed that neutral soaps significantly increased bond strength and decreased microleakage of dentin bonding agents. The aim of this study was histopathological evaluation of the effect of sodium sulfonate application as neutral soap on the cat's dental pulp after an ideal composite restorative treatment .  Methods: Ten adult cats with 40 caries-f...

Abstract We study the problem of computing the dimension of a left/right ideal in a group algebra F[G] of a finite group G over a field F, by relating the dimension to the rank of an appropriatematrix, originating from a regular right/left representation of G. In particular, the dimension of a principal ideal is equal to the rank of the matrix representing a generator. From this observation, we...

a module m is called epi-retractable if every submodule of m is a homomorphic image of m. dually, a module m is called co-epi-retractable if it contains a copy of each of its factor modules. in special case, a ring r is called co-pli (resp. co-pri) if rr (resp. rr) is co-epi-retractable. it is proved that if r is a left principal right duo ring, then every left ideal of r is an epi-retractable ...

In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak...

In this paper, we introduce the theory of Rota-Baxter operators on Clifford semigroups, useful tools for obtaining dual weak braces, i.e., triples $\left(S,+,\circ\right)$ where $\left(S,+\right)$ and $\left(S,\circ\right)$ are semigroups such that $a\circ\left(b+c\right) = a\circ b - a +a\circ c$ $a\circ a^- -a+a$, all $a,b,c\in S$. To each algebraic structure is associated set-theoretic solut...