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The Open Webinar--Idempotent factorization of matrices over integral domains: an overview

主 讲 人 :Laura Cossu    博士

活动时间:04月09日19时00分    

地      点 :钉钉群

讲座内容:

A classical openproblem in ring theory is to characterize the integral domains R suchthat every singular matrix over R is a product of idempotent matrices. Theimportance of this problem is underlined by the inter-connections with otherbig unsolved questions: Classify integral domains whose general linear groupsare generated by the elementary matrices and those verifying “weaker” versionsof

the Euclideanalgorithm. In fact, over a Bézout domain, every singular matrix can be writtenas a product of  idempotent factors ifand 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 ofclassical results and recent developments on the factorization of matrices intoidempotents. In particular, we will consider products of idempotent matricesover special classes of non-Euclidean principal ideal domains and over integraldomains that are not Bézout.


主讲人介绍:

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-established internationaljournals. She has given courses of mathematics for the bachelor degree inBiology and of Algebra for the bachelor degree in Mathematics at the Universityof Padova.


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