A ring $R$ with identity is called ``clean'' if $~$for every element $ain R$, there exist an idempotent $e$ and a unit $u$ in $R$ such that $a=u+e$. Let $C(R)$ denote the center of a ring $R$ and $g(x)$ be a polynomial in $C(R)[x]$. An element $rin R$ is called ``g(x)-clean'' if $r=u+s$ where $g(s)=0$ and $u$ is a unit of $R$ and, $R$ is $g(x)$-clean if every element is $g(x)$-clean. In this pa...

The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topolo...

in this paper, we give some new definitions of m-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete m-fuzzy metric spaces.

in this paper we study some results on noetherian semigroups. we  show that if  $s_s$ is an  strongly  faithful $s$-act and $s$ is a duo weakly noetherian, then we have the following.

Active sensing organisms, such as bats, dolphins, and weakly electric fish, generate a 3-D space for active sensation by emitting self-generated energy into the environment. For a weakly electric fish, we demonstrate that the electrosensory space for prey detection has an unusual, omnidirectional shape. We compare this sensory volume with the animal's motor volume--the volume swept out by the b...

A Banach space E has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space P(kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric k-fold projective tensor product of E (i.e., the predual of P...

We introduce partial actions of weakly left E-ample semigroups, thus extending both the notion of partial actions of inverse semigroups and that of partial actions of monoids. Weakly left E-ample semigroups arise very naturally as subsemigroups of partial transformation semigroups which are closed under the unary operation α 7→ α, where α is the identity map on the domain of α. We investigate t...