Let R be a commutative local k-algebra of Krull dimension one, where k is field. α automorphism R, and define S to the skew polynomial algebra R[θ;α]. We offer, under some additional assumptions on criterion for have injective hulls all simple S-modules locally Artinian - that is, satisfy property (⋄). It easy well known if finite order, then has this property, but in order get when infinite we...

Let R be a ring, α an automorphism, and δ an α-derivation of R. If the classical quotient ring Q of R exists, then R is weak α-skew Armendariz if and only if Q is weak α-skew Armendariz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly ci...

Exploitation of the NP hard, mixed μ problem structure provides a polynomial time algorithm that approximates μ with usually reasonable answers. When the problem is extended to the skew μ problem an extension of the existing method to the skew μ formulation is required. The focus of this paper is to extend the μ upper bound derivation to the skew μ upper bound and show its direct computation by...

In most cases beam is injected into electron storage rings in the horizontal plane and off-axis. The larger the horizontal emittance of the injected beam the larger the acceptance of the ring has to be. The injected beam is usually delivered by a synchrotron. In case the vertical acceptance of the ring is sufficiently large one can take advantage of the small vertical emittance reached in well ...

Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:Irightarrow R$ be an additivemap. Then skew-Engel condition $langle... langle langle$$f(x),x^{n_1} rangle,x^{n_2} rangle ,...,x^{n_k} rangle=0$ implies that $f (x)=0$ $forall,xin I$ provided $2neq$ char $(R)>n_1+n_2+...+n_k, $ where $n_1,n_2,...,n_k$ are natural numbers. This extends some existing results. In the end, we also gener...

Linear codes may be endowed with cyclic structures by means of skew polynomial rings. This is the case of Piret cyclic convolutional codes [26] and the subsequent generalizations and alternatives (see [27], [14], [11], [25], [16], [20]). Non commutative cyclic structures of this kind have been also considered for block linear codes ([7], [5], [4], [12], [1]), and for linear codes over commutati...