We will consider Multiplication operators on Hilbert spaces of analyticfunctions on a domain $\omega \subset \cmark $. We determine the commutants of certainMultiplication operators with adjoints in a Cowen-Douglas class operator.

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In this paper, we investigate the properties of the reduced minimum modulus in the context of Banach spaces. Given a Banach space $X$, we denote the algebra of bounded operators on $X$ as $B(X)$. Our primary focus is on examining the relationship between the reduced minimum modulus of a given operator $T \in B(X)$ and its associated left and right Multiplication operators, denoted by $L_T: S \mapsto TS$ and $R_T: S \mapsto ST$, respectively. By analyzing these relationships, we present a comprehensive analysis of their properties and derive novel results concerning the reduced minimum modulus of $L_T$ and $R_T$.

In this paper we introduce the concept of Multiplication-like modules and we obtain some related results. We show that an R-module M is Multiplication-like if and only if for each ideal I of R, I = (IM: R M). We prove that any Multiplication-like module is faithful and r-Multiplication. So we get that any at and Multiplication-like module is faithfully at.

Let M be a lattice module over the multiplicative lattice L. An L-module M is called a Multiplication lattice module if for every element NÎM there exists an element aÎL such that N=a1M. Our objective is to investigate properties of prime elements of Multiplication lattice modules.