×

Isomorphisms between Morita context rings. (English) Zbl 1258.16040

The paper investigates isomorphisms between Morita rings associated to two Morita contexts. Two classes of such isomorphisms are introduced and characterized by using the \(\mathbb Z\)-graded structure of the Morita rings. If the rings in the two Morita contexts have only trivial idempotents and all the Morita maps are zero, the isomorphisms of these two classes are proved to be the only isomorphisms between the two Morita rings.

MSC:

16W20 Automorphisms and endomorphisms
16S50 Endomorphism rings; matrix rings
16W50 Graded rings and modules (associative rings and algebras)
15A30 Algebraic systems of matrices
16D90 Module categories in associative algebras
16D20 Bimodules in associative algebras
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] DOI: 10.1016/j.laa.2010.10.007 · Zbl 1222.16017
[2] DOI: 10.1007/BF01199113 · Zbl 0674.16014
[3] DOI: 10.1006/jabr.2000.8328 · Zbl 0964.16031
[4] DOI: 10.1016/0024-3795(93)90255-M · Zbl 0810.16027
[5] Coelho SP, Arch. Math. (Basel) 61 pp 119– (1993) · Zbl 0785.16020
[6] DOI: 10.1090/S0002-9939-96-03172-3 · Zbl 0848.16022
[7] Dicks W, Automorphisms of the Free Algebra of Rank Two (1985) · Zbl 0574.16021
[8] Faith C, Algebra II: Ring Theory (1976)
[9] DOI: 10.1016/0024-3795(80)90221-9 · Zbl 0434.16015
[10] DOI: 10.1007/BF01194296 · Zbl 0601.16028
[11] DOI: 10.1016/0021-8693(91)90206-N · Zbl 0729.16024
[12] DOI: 10.1016/0024-3795(90)90121-R · Zbl 0706.15016
[13] DOI: 10.1155/S0161171203205251 · Zbl 1022.16019
[14] DOI: 10.1016/0024-3795(94)00309-2 · Zbl 0861.16019
[15] McConnell JC, Noncommutative Noetherian Rings (1987)
[16] Năstăsescu C, Methods of Graded Rings, Lecture Notes in Mathematics 1836 (2004)
[17] Rosenberg A, Pac. J. Math. 11 pp 1109– (1961)
[18] Rotman JJ, Advanced Modern Algebra (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.