Tang, Gaohua; Li, Chunna; Zhou, Yiqiang Study of Morita contexts. (English) Zbl 1292.16020 Commun. Algebra 42, No. 4, 1668-1681 (2014). Summary: This article concerns mainly various ring properties of Morita contexts. Necessary and sufficient conditions are obtained for a general Morita context or a trivial Morita context or a generalized matrix ring over a ring to satisfy a certain ring property which is among being semilocal, semiperfect, left perfect, semiprimary, semipotent, potent, clean, strongly \({\pi}\)-regular, semiregular, etc. Many known results on a formal triangular matrix ring are extended to a Morita context or a trivial Morita context. Some questions on this subject raised by K. Varadarajan [in Math. Stud. 2007, 81-99 (2007; Zbl 1185.16032)] are answered. Cited in 33 Documents MSC: 16S50 Endomorphism rings; matrix rings Keywords:formal triangular matrix rings; generalized matrix rings over rings; Morita contexts Citations:Zbl 1185.16032 PDFBibTeX XMLCite \textit{G. Tang} et al., Commun. Algebra 42, No. 4, 1668--1681 (2014; Zbl 1292.16020) Full Text: DOI References: [1] DOI: 10.1016/0021-8693(71)90034-2 · Zbl 0221.16014 [2] DOI: 10.1007/978-1-4612-4418-9 [3] Azumaya G., J. Fac. Sci. Hokkaido Univ. Ser. I. 13 pp 34– (1954) [4] DOI: 10.1090/S0002-9939-1950-0034757-7 [5] DOI: 10.1080/00927870209342393 [6] Dischinger F., C. R. Acad. Sci. Paris Ser. A 283 pp 571– (1976) [7] Goodearl K. R., Ring Theory (1976) [8] Nicholson W. K., Comm. Alg. 20 pp 2589– (2001) [9] DOI: 10.1080/00927879908826443 · Zbl 0921.16002 [10] DOI: 10.1080/00927879908826770 · Zbl 0941.16005 [11] DOI: 10.1016/S0022-4049(98)00129-7 · Zbl 0951.16009 [12] DOI: 10.1007/s10469-008-9016-y · Zbl 1155.16302 [13] DOI: 10.1007/s10958-010-0133-5 · Zbl 1283.16025 [14] DOI: 10.1007/978-1-4419-8616-0 [15] Loustaunau P., Morita Contexts. Noncommutative Ring Theory (Athens, OH, 1989) (1990) [16] DOI: 10.1080/00927878708823519 · Zbl 0629.16013 [17] McConnell J. C., Noncommutative Noetherian Rings (1987) · Zbl 0644.16008 [18] Morita K., Sci. Rep. Tokyo Kyoiku Diagaku Sect. 6 pp 83– (1958) [19] Nicholson W. K., Trans. AMS. 207 pp 361– (1975) [20] DOI: 10.1090/S0002-9947-1977-0439876-2 [21] DOI: 10.1016/0021-8693(73)90143-9 · Zbl 0253.16007 [22] Varadarajan , K. ( 2008 ). Formal triangular matrix rings and modules over them: A survey.Math. Student 2007, Special Centenary Volume: 81–99 . · Zbl 1185.16032 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.