Invertible commutators in matrix rings

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DC Field	Value	Language
dc.contributor.author	Khurana, Dinesh	-
dc.date.accessioned	2013-04-29T11:53:35Z	-
dc.date.available	2013-04-29T11:53:35Z	-
dc.date.issued	2011	-
dc.identifier.citation	J. Alg. Appl. 10 (1) pp.,51-71	en_US
dc.identifier.uri	http://www.worldscientific.com/doi/abs/10.1142/S0219498811004422	en_US
dc.identifier.uri	http://hdl.handle.net/123456789/62	-
dc.description	Only IISERM authors are available in the record.	-
dc.description.abstract	In a matrix ring R = 𝕄2(S) where S is a commutative ring, we study equations of the form XY - YX = U ∈ GL2(S), focusing on matrices in R that can appear as X or as XY in such equations. These are the completable and the reflectable matrices in R. For matrices A ∈ R with a zero row or with a constant diagonal, explicit and "computer-checkable" criteria are found for A to be completable or reflectable. A formula for det (XY - YX) discovered recently with Shomron connects this study to diophantine questions about the representation of units of the ground ring S by quadratic forms of the type px2 +qy2.	en_US
dc.language.iso	en	en_US
dc.subject	Matrix rings	en_US
dc.subject	additive commutators	en_US
dc.subject	completable and reflectable matrices	en_US
dc.title	Invertible commutators in matrix rings	en_US
dc.type	Article	en_US
Appears in Collections:	Research Articles

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