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Article

Chen, Huanyin ; Chen, Miaosen
Extensions of $GM$-rings. (English). Czechoslovak Mathematical Journal, vol. 55 (2005), issue 2, pp. 273-281
MSC: 16E50, 16S50, 16U60, 16U99 | MR 2137137 | Zbl 1081.16016
Keywords:
$GM$-ring; module extension; power series ring
Summary:
It is shown that a ring $R$ is a $GM$-ring if and only if there exists a complete orthogonal set $\lbrace e_1,\cdots ,e_n\rbrace $ of idempotents such that all $e_iRe_i$ are $GM$-rings. We also investigate $GM$-rings for Morita contexts, module extensions and power series rings.
References:
[1] V. P. Camillo and H. P. Yu: Exchange rings, units and idempotents. Comm. Algebra 22 (1994), 4737–4749. DOI 10.1080/00927879408825098 | MR 1285703
[2] H. Chen: Exchange rings with artinian primitive factors. Algebras Represent. Theory 2 (1999), 201–207. MR 1702275 | Zbl 0960.16009
[3] H. Chen: Rings with many idempotents. Internat. J.  Math. Math. Sci. 22 (1999), 547–558. DOI 10.1155/S0161171299225471 | MR 1717176 | Zbl 0970.16004
[4] H. Chen: Units, idempotents and stable range conditions. Comm. Algebra 29 (2001), 703–717. DOI 10.1081/AGB-100001535 | MR 1841993 | Zbl 0989.16007
[5] H. Chen: Stable ranges for Morita contexts. SEA  Bull. Math. 25 (2001), 209–216. DOI 10.1007/s10012-001-0209-8 | MR 1935091 | Zbl 0999.16005
[6] K. R. Goodearl and P. Menal: Stable range one for rings with many units. J.  Pure Appl. Algebra 54 (1988), 261–287. DOI 10.1016/0022-4049(88)90034-5 | MR 0963548
[7] A. Haghany: Hopficity and co-hopficity for Morita contexts. Comm. Algebra 27 (1999), 477–492. DOI 10.1080/00927879908826443 | MR 1668301 | Zbl 0921.16002
[8] J. Han and W. K. Nicholson: Extensions of clean rings. Comm. Algebra 29 (2001), 2589–2595. DOI 10.1081/AGB-100002409 | MR 1845131
[9] M. Henriksen: Two classes of rings generated by their units. J.  Algebra 31 (1974), 182–193. DOI 10.1016/0021-8693(74)90013-1 | MR 0349745 | Zbl 0285.16009
[10] Y. Hirano: Another triangular matrix ring having Auslander-Gorenstein property. Comm. Algebra 29 (2001), 719–735. DOI 10.1081/AGB-100001536 | MR 1841994 | Zbl 0992.16013
[11] P. Menal: On $\pi $-regular rings whose primitive factor rings are artinian. J.  Pure. Appl. Algebra 20 (1981), 71–78. DOI 10.1016/0022-4049(81)90049-9 | MR 0596154 | Zbl 0457.16006
[12] W. K. Nicholson: Strongly clean rings and Fitting’s lemma. Comm. Algebra 27 (1999), 3583–3592. DOI 10.1080/00927879908826649 | MR 1699586 | Zbl 0946.16007
[13] W. K. Nicholson and K. Varadarjan: Countable linear transformations are clean. Proc. Amer. Math. Soc. 126 (1998), 61–64. DOI 10.1090/S0002-9939-98-04397-4 | MR 1452816
[14] E. Pardo: Comparability, separativity, and exchange rings. Comm. Algebra 24 (1996), 2915–2929. DOI 10.1080/00927879608825721 | MR 1396864 | Zbl 0859.16001
[15] T. Wu and W. Tong: Stable range condition and cancellation of modules. Pitman Res. Notes Math. 346 (1996), 98–104. MR 1396566
[16] H. P. Yu: On the structure of exchange rings. Comm. Algebra 25 (1997), 661–670. DOI 10.1080/00927879708825882 | MR 1428806 | Zbl 0873.16007
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