Modules (co)reduced relative to another module

2024/04/10 by Tilahun Abebaw, Amanuel Mamo, Abebaw, Tilahun +5
Mathematics · #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2404.06874

Abstract

Let R be a commutative unital ring, \mathfrak a an ideal of R and M a fixed R-module. We introduce and study generalisations of \mathfraka-reduced modules, \mathfrakR_\mathfrak a and \mathfraka-coreduced modules, \mathfrakC_\mathfrak a studied in the literature. They are called modules \mathfrak a-reduced with respect to M, \mathfrakR^M_\mathfrak a and modules \mathfrak a-coreduced with respect to M, \mathfrakC^M_\mathfrak a. The paper lifts several known results about \mathfrakR_\mathfrak a and \mathfrakC_\mathfrak a to larger classes of modules \mathfrakR^M_\mathfrak a and \mathfrakC^M_\mathfrak a respectively. Results about \mathfrakR_\mathfrak a and \mathfrakC_\mathfrak a can be retrieved by taking M= R.

Related

• Applications of reduced and coreduced modules III: homological properties and coherence of functors
• Applications of reduced and coreduced modules II: Radicality of the functor Hom_R(R/I, -)
• Applications of reduced and coreduced modules I
• z^∘-submodules of a reduced multiplication module
• Quasi z^∘-submodules of a reduced multiplication