The Open Webinar--Idempotent factorization of matrices over integral domains: an overview
主 讲 人 ：Laura Cossu 博士
地 点 ：钉钉群
A classical open problem in ring theory is to characterize the integral domains R such that every singular matrix over R is a product of idempotent matrices. The importance of this problem is underlined by the inter-connections with other big unsolved questions: Classify integral domains whose general linear groups are generated by the elementary matrices and those verifying “weaker” versions of the Euclidean algorithm. In fact, over a Bézout domain, every singular matrix can be written as a product of idempotent factors if and only if every invertible matrix can be written as a product of elementary matrices . Moreover, this happens if and only if the domain admits a weak algorithm.
In our talk, we will give an overview of classical results and recent developments on the factorization of matrices into idempotents. In particular, we will consider products of idempotent matrices over special classes of non-Euclidean principal ideal domains and over integral domains that are not Bézout.
Laura Cossu iscurrently a fixed-term lecturer in Algebra at the University of Padova (Italy).She graduated with a Master’s degree in Differential Geometry at the Universityof Cagliari and obtained a Ph.D. degree in Algebra from the University ofPadova on October 2017. During her Ph.D. and the subsequent post-doc in Padova,she has worked in the field of commutative ring theory. Her research interests include matrix theory over integraldomains and the study of factorization and divisibility properties ofcommutative rings. She has published five articles on well-establishedinternational journals. She has given courses of mathematics for the bachelordegree in Biology and of Algebra for the bachelor degree in Mathematics at theUniversity of Padova.