let $mathcal{a}$ be a banach algebra with bai and $e$ be an introverted subspace of $mathcal{a'}$.in this paper we study the quotient arens regularity of $mathcal{a}$ with respect to $e$ and prove that the group algebra $l^1(g)$ for a locally compact group $g$, is quotient arens regular with respect to certain introverted subspace $e$ of $l^infty(g)$.some related result are given as well.

Let R be a ring. A right R-module is said to C-flat if the kernel of any epimorphism B → C-pure in B, i.e. induced map Hom(C,B) Hom(C,A) surjective for cyclic C. Projective modules are and weakly-flat neat-flat. In this article, it discussed connections between C-flat, weakly-flat, neat-flat singly flat modules. It shown that coincide with singly-projective over arbitrary rings. Next, several c...

This is a systematic study of the behaviour finite coverings (affine) schemes with regard to two Grothendieck topologies: canonical topology and fpqc topology. The history problem takes roots in foundations topologies, passes through main strides Commutative Algebra leads new Mathematics up perfectoids prisms. We first review affine show, keeping Olivier's lost work, that it coincides effecti...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

We introduce in this paper the concept of left WMC2 rings and concern ourselves with rings containing an injective maximal left ideal. Some known results for left idempotent reflexive rings and left HI rings can be extended to left WMC2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with nonzero socle and extend some known results on ...

We show that the properties of being injective, surjective, continuous, strongly surjective, stably solvable, carry over to weakly-near maps. We also prove a data dependence theorem for equations of the form A(x) = z, where A is weakly-near to some bijective map.

The class of weakly algebrizable logics is defined as the class of logics having monotonic and injective Leibniz operator. We show that “monotonicity” cannot be discarded on this definition, by presenting an example of a system with injective and non monotonic Leibniz operator. We also show that the non injectivity of the non protoalgebraic inf-sup fragment of the Classic Propositional Calculus...