Let R be a commutative ring with unity, M unitary R-module and G finite abelian group (viewed as \({\mathbb {Z}}\)-module). The main objective of this paper is to study properties mod-annihilators M. For \(x \in M\), we the ideals \([x : M] =\{r\in ~|~ rM\subseteq Rx\}\) corresponding mod-annihilator We investigate when [x an essential ideal R. prove that arbitrary intersection represented by i...

be the set of (iso-classes of) finite dimensional simple right A-modules. An ndimensional simple A-module V ∈ Simpn(A) defines a surjectiv homomorphism of k-algebras, ρ : A → Endk(V ), the kernel of which is a two-sided maximal ideal mV , of A. Let Max≤∞ be the set of all such maximal ideals of A, for n ≥ 1. To exclude some strange and for our purposes non-interesting cases, we shall assume tha...

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...