Let A be a ring with identity. The generalized affine transformation monoid Gaff(A) is defined as the set of all transformations on A of the form x → xu + a (for all x ∈ A), where u,a∈ A. We study the algebraic structure of the monoid Gaff(A) on a finite Galois ring A. The following results are obtained: an explicit description of Green’s relations on Gaff(A); and an explicit description of the...

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C-ternary ring homomorphisms associated to the Trif functional equation d · C d−2f( x1 + · · ·+ xd d ) + C d−2 d ∑

The purpose of the present paper is to classify generalized derivations satisfying more specific algebraic identities in a prime ring with
 involution second kind. Some well-known results
 characterizing commutativity rings by have
 been using derivation.

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C-ternary ring homomorphisms associted to the Trif functional equation d · C d−2f( x1 + · · ·+ xd d ) + C d−2 d ∑

Based on a coin-tossing scheme, a generalized Mahonian statistic is defined on absorption ring mappings and applied in obtaining combinatorial interpretations of the coefficient of q j in the expansion of > k i=1 (1+q+q 2 + } } } +q m i). In the permutation case, the statistic coincides with one studied by Han that specializes many known Mahonian statistics.

In this paper, the structure of the ideals in the ring of Colombeau generalized numbers is investigated. Connections with the theories of exchange rings, Gelfand rings and lattice-ordered rings are given. Characterizations for prime, projective, pure and topologically closed ideals are given, answering in particular the questions about prime ideals in [1]. Also z-ideals in the sense of [21] are...

We prove some theorems in the setting of a 3-prime near-ring admitting a suitably constrained generalized derivation, thereby extending some known results on derivations. Moreover, we give an example proving that the hypothesis of 3-primeness is necessary.

Abstract In this note, we prove the semiampleness conjecture for Kawamata log terminal Calabi–Yau (CY) surface pairs over an excellent base ring. As applications, deduce that generalized abundance and Serrano’s hold surfaces. Finally, study CY threefolds a mixed characteristic DVR.

Let $S=End(M)$ be the ring of endomorphisms a right $R$-module M. In this paper we define minus parital order for endomorphism modules. Also, extend study partial to (Rickart) module. Thus several well-known results concerning are generalized.

We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of J.F. Colombeau and establish the inverse Cauchy-Schwarz inequality in this context. As an application, we prove a dominant energy condition for some energy tensors as put forward in Hawking and Ellis’s book “The large scale structure of space-time”. Our work is based on a new character...