Monomorphisms in the category of firm modules. Issue 4 (2nd April 2020)

• Record Type: Journal Article
• Authors: Väljako, Kristo
• Is Part Of: Communications in algebra. Volume 48:Issue 4(2020)
• Page Start: 1528
• Page End: 1537
• Publication Date: 2020-04-02
• Subjects: Idempotent ring -- firm module -- unitary module -- monomorphism -- regular monomorphism; 16D90; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1691570
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: In this article, we consider the category of unitary right modules over an (associative) ring and the category of firm right modules over an idempotent ring. We study monomorphisms in these categories and give conditions under which morphisms are monomorphisms in the category of firm modules. We also prove that the lattice of categorically defined subobjects of a firm module is isomorphic to the lattice of unitary submodules of that module.