On Baer type criterion for $C$-dense‎, ‎$C$-closed and quasi injectivity

on baer type criterion for $c$-dense‎, ‎$c$-closed and quasi injectivity

‎for the subclasses ${mathcal m}_1$ and ${mathcal m}_2$ of‎‎monomorphisms in a concrete category $mathcal c$‎, ‎if ${mathcal‎‎m}_2subseteq {mathcal m}_1$‎, ‎then ${mathcal m}_1$-injectivity‎‎implies ${mathcal m}_2$-injectivity‎. ‎the baer type criterion is about‎ ‎the converse of this fact‎. ‎in this paper‎, ‎we apply injectivity to the classes of {it $c$-dense‎, ‎$c$-closed}‎ ‎monomorphisms‎. ...

On quasi-baer modules

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

Extensions of Baer and quasi-Baer modules

On p-injectivity, YJ-injectivity and quasi-Frobeniusean rings

A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

K1-injectivity for Properly Infinite C ∗-algebras

One of the main tools to classify C∗-algebras is the study of its projections and its unitaries. It was proved by Cuntz in [Cun81] that if A is a purely infinite simple C∗-algebra, then the kernel of the natural map for the unitary group U(A) to the Ktheory groupK1(A) is reduced to the connected component U(A), i.e. A isK1-injective (see §3). We study in this note a finitely generated C∗-algebr...

BAER AND QUASI-BAER PROPERTIES OF SKEW PBW EXTENSIONS

A ring $R$ with an automorphism $sigma$ and a $sigma$-derivation $delta$ is called $delta$-quasi-Baer (resp., $sigma$-invariant quasi-Baer) if the right annihilator of every $delta$-ideal (resp., $sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=sigma(R)leftlangle x...