CORDIS Project
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The project investigates the factorization of singular matrices into idempotent matrices within integral domains. It aims to explore the nonuniqueness of these factorizations and connect two previously unrelated areas of ring theory, enhancing understanding of matrix rings and their properties.
The characterization of integral domains R such that every singular matrix over R is a product of idempotent matrices is a classical open problem in ring theory.
Its importance lies in the inter-connections with other big unsolved issues: classify integral domains whose general linear groups are generated by the elementary matrices, and those fulfilling weak versions of the Euclidean algorithm.
The study of idempotent factorizations in matrix rings has gained increasing attention over the years…
UNIVERSITAET GRAZ
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