It is shown that the Baer–Kaplansky Theorem can be extended to all abelian groups provided rings of endomorphisms are replaced by trusses corresponding heaps. That is, every group determined up isomorphism its endomorphism truss and between two associated some [Formula: see text] induced an element from text]. This correspondence then modules over a ring considering heaps modules. proved heap m...

Abstract The aim of the paper is to generalize decomposition theorems showed in Bagheri-Bardi et al. (Linear Algebra Appl 583:102–118, 2019; Linear 539:117–133, 2018) by a unified approach. We show general theorem with respect hereditary property. Then vast majority decompositions known algebra Hilbert space operators generalized elements Baer $$*$$ <mml:math xmlns:mml="http://www.w3.org/1998/M...

Suppose that G is a finite group and x ∈ G has prime order p ≥ 5. Then x is contained in the solvable radical of G, O∞(G), if (and only if) 〈x, xg〉 is solvable for all g ∈ G. If G is an almost simple group and x ∈ G has prime order p ≥ 5, then this implies that there exists g ∈ G such that 〈x, xg〉 is not solvable. In fact, this is also true when p = 3 with very few exceptions, which are describ...

A group is said to have a finite covering by subgroups if it is the set theoretic union of finitely many subgroups. A theorem of B. H. Neumann [11] characterizes groups with finite coverings by proper subgroups as precisely those groups with finite non-cyclic homomorphic images. R. Baer (see [13, Theorem 4.16]) proved that a group has a finite covering by abelian subgroups if and only if it is ...

An ideal I of a ring R is called right Baer-ideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R is a right Baer-ideal, R is n-generalized right quasi-Baer if for each I E R the ideal In is right Baer-ideal, and R is right principaly quasi-Baer if every principal right ideal of R is a right Baer-ideal. Therefore the concept of Baer idea...

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, ....

A group is called capable if it is a central factor group. We consider the capability of nilpotent products of cyclic groups, and obtain a generalisation of a theorem of Baer for the small class case. The approach may also be used to obtain some recent results on the capability of certain nilpotent groups of class 2. We also obtain a necessary condition for the capability of an arbitrary p-grou...

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...