Zero product and zero Jordan product determined Munn algebras
Bo Yu, Kaijia Luo, Jiankui Li

TL;DR
This paper investigates the algebraic structure of Munn algebras, showing they are generated by products of commutators and Jordan products of idempotents, and characterizes when they are zero product determined.
Contribution
It establishes new results on the generation and structure of Munn algebras, including conditions for being zero product determined and expressibility via commutators and Jordan products.
Findings
Every element is a sum of finite products of commutators.
Estimated the minimal number of such products needed.
Proved Munn algebras are additively spanned by Jordan products of idempotents under certain conditions.
Abstract
Let be the ring of all matrices over a division ring , with the product given by , where is a fixed matrix over . When and , we demonstrate that every element in is a sum of finite products of pairs of commutators. We also estimate the minimal number such that . Furthermore, if , we prove that is additively spanned by Jordan products of idempotents. For a field with , we show that the Munn algebra is zero product determined and zero Jordan product…
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic · Advanced Operator Algebra Research
