Let R be a ring. An element a in R is called left morphic (Nicholson and Sánchez Campos, 2004a) if l a R/Ra, where l a denotes the left annihilator of a in R. The ring itself is called a left morphic ring if every element is left morphic. Left morphic rings were first introduced by Nicholson and Sánchez Campos (2004a) and were discussed in great detail there and in Nicholson and Sánchez Campos ...

A skew generalized power series ring R[[S, ω]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are...

The classical lattice A ,*, whose Voronoi cells tile Euclidean n-space by permutohedra, can be given the generalized balance ternary ring structure GBT, in a natural way as a quotient ring of Z [xl. The ring GBT, can also be considered as the set of all finite sequences sO sl.. . sk, with si E GBT,/srGBT, for all i, where M is an appropriately chosen element in GBT,. The extended generalized ba...

‎we call a ring $r$ right generalized semiperfect if every simple right $r$-module is an epimorphic image of a flat right $r$-module with small kernel‎, ‎that is‎, ‎every simple right $r$-module has a flat $b$-cover‎. ‎we give some properties of such rings along with examples‎. ‎we introduce flat strong covers as flat covers which are also flat $b$-covers and give characterizations of $a$-perfe...

An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with exponents in an ordered monoid. We study when a generalized power series ring has a Rota-Baxter operator and how this is related to the ordered monoid.

The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized greatest common divisor are presented. Applications to finite simple continued fraction expansion of rational numbers and Smith normal form of integral matrices with an integer parameter are also given.

Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.

The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized GCD are presented. Applications to finite simple continued fraction expansion and Smith normal form of integral matrices with integer parameters are also given.