Enlargements of rings. Issue 4 (21st November 2020)

• Record Type: Journal Article
• Authors: Laan, Valdis; Väljako, Kristo
• Is Part Of: Communications in algebra. Volume 49:Issue 4(2021)
• Page Start: 1764
• Page End: 1772
• Publication Date: 2020-11-21
• Subjects: Enlargement -- Morita context -- Morita equivalence -- ring; 16D90; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1851702
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: We introduce enlargements of rings as additive analogues of enlargements of semigroups. For example, a full matrix ring over an idempotent ring is an enlargement of that ring. As our main result we prove that two idempotent rings are Morita equivalent if and only if they have a joint enlargement. We also give a necessary and sufficient condition for a ring with left local units to be Morita equivalent to a ring with identity. That condition means that a ring is an enlargement of its local subring.