Department of Mathematics,
University of California San Diego
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Math 211A: Algebra Seminar
Professor Meltem Altun Ozarslan
UC Irvine; Hacettepe University
Finite versus Full Exchange: Theory and Open Problems
Abstract:
The exchange property, introduced by Crawley and Jonsson in 1964 in the study of direct decompositions of algebraic systems and later extended to modules and rings by Warfield, plays a central role in modern decomposition theory. One of the main open problems in the area is whether the finite exchange property implies the full exchange property. This talk surveys the development of exchange theory from its module-theoretic origins to its ring-theoretic formulation via exchange rings. The last part of the talk is based on joint work with A. Cigdem Ozcan and focuses on lifting theory, including idempotent, regular, and unit lifting ideals and morphisms, and their interaction with local morphisms.
Host: Lucas Buzaglo
February 2, 2026
3:00 PM
APM 7321
Research Areas
Algebra****************************
