Results 21 to 25 of about 60 (25)

A note on $σ$-reversibility and $σ$-symmetry of skew power series rings [PDF]

International Journal of Algebra, Vol. 3, 2009, no. 9, 435 - 442, 2009
Let $R$ be a ring and $\sigma$ an endomorphism of $R$. In this note, we study the transfert of the symmetry ($\sigma$-symmetry) and reversibility ($\sigma$-reversibility) from $R$ to its skew power series ring $R[[x;\sigma]]$. Moreover, we study on the relationship between the Baerness, quasi-Baerness and p.p.-property of a ring $R$ and these of the ...
arxiv  

On McCoy Condition and Semicommutative Rings [PDF]

Comment.Math.Univ.Carolin. 54,3 (2013) 329-337, 2012
Let $R$ be a ring, $\sigma$ an endomorphism of $R$, $I$ a right ideal in $S=R[x;\sigma]$ and $M_R$ a right $R$-module. We give a generalization of McCoy's Theorem \cite{mccoy}, by showing that, if $r_S(I)$ is $\sigma$-stable or $\sigma$-compatible. Then $\;r_S(I)\neq 0$ implies $r_R(I)\neq 0$. As a consequence, if $R[x;\sigma]$ is semicommutative then $
arxiv  

Lie nilpotency indices of symmetric elements under oriented involutions in group algebras [PDF]

arXiv, 2012
Let $G$ be a group and let $F$ be a field of characteristic different from 2. Denote by $(FG)^+$ the set of symmetric elements and by $\mathcal{U}^+(FG)$ the set of symmetric units, under an oriented classical involution of the group algebra $FG$. We give some lower and upper bounds on the Lie nilpotency index of $(FG)^+$ and the nilpotency class of ...
arxiv  

A constructive counterpart of the subdirect representation theorem for reduced rings [PDF]

arXiv
We give a constructive counterpart of the theorem of Andrunakievi\v{c} and Rjabuhin, which states that every reduced ring is a subdirect product of domains. As an application, we extract a constructive proof of the fact that every ring $A$ satisfying $\forall x\in A. x^3=x$ is commutative from a classical proof.
arxiv  

Positive spoof Lehmer factorizations [PDF]

arXiv
We investigate the integer solutions of Diophantine equations related to Lehmer's totient conjecture. We give an algorithm that computes all nontrivial positive spoof Lehmer factorizations with a fixed number of bases $r$, and enumerate all nontrivial positive spoof Lehmer factorizations with 6 or fewer factors.
arxiv