We construct a generating set for the ring of invariants for the four and five dimensional indecomposable modular representations of a cyclic group of prime order. We then observe that for the four dimensional representation the ring of invariants is generated in degrees less than or equal to 2p − 3, and for the five dimensional representation the ring of invariants is generated in degrees less...

the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.

We study the ring of polyfunctions over Z/nZ. The a commutative R with unit element is functions f:R→R which admit polynomial representative p∈R[x] in sense that f(x)=p(x) for all x∈R. This allows to define invariant s associates value N∪{∞}. function generalizes number theoretic Smarandache function. For R=Z/nZ we provide unique representation polynomials vanish as yields new formula Ψ(n) also...

A $\ast$-ring
 $R$ is called a $\pi$-Baer $\ast$-ring, if for any projection invariant left ideal $Y$ of $R$, the right annihilator $Y $
 generated, as ideal, by projection.
 In this note, we
 study some properties such $\ast$-rings.
 We indicate interrelationships between $\ast$-rings and related classes rings as
 rings, Baer $\ast$-rings, quasi-Baer $\ast$-rings....

We use the concept of a regular object with respect to another object in an arbitrary category, defined in [3], in order to obtain the transfer of regularity in the sense of Zelmanowitz between the categories R−mod and S−mod, when S is an excellent extension of the ring R. Consequently, we obtain a result of [5]: if S is an excellent extension of the ring R, then S is von Neumann regular ring i...

We study a particular graded ring structure on the set of all loopfree matroids on a fixed labeled ground set, which occurs naturally in tropical geometry. The product is given by matroid intersection and the additive structure is defined by assigning to each matroid the indicator vector of its chains of flats. We show that this ring is generated in corank one, more precisely that any matroid c...

In Section 2, after giving the basic definitions and some elementary consequences, we introduce two fundamental algebraic structures associated with a coherent configuration, namely, the boolean algebra of admissable relations and the adjacency ring. The action of a group on a finite set induces the structure of a coherent configuration in the set, and in this situations, which we refer to as t...

Given a fiber bundle of GKM spaces, π : M → B, we analyze the structure of the equivariant K-ring of M as a module over the equivariant K-ring of B by translating the fiber bundle, π, into a fiber bundle of GKM graphs and constructing, by combinatorial techniques, a basis of this module consisting of K-classes which are invariant under the natural holonomy action on the K-ring of M of the funda...