Geodesic
Extensions of $GM$-rings
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 273-281
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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.
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.
Classification : 16E50, 16S50, 16U60, 16U99
Keywords: $GM$-ring; module extension; power series ring 
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Chen, Huanyin; Chen, Miaosen. Extensions of $GM$-rings. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 273-281. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a0/

[1] V. P. Camillo and H. P. Yu: Exchange rings, units and idempotents. Comm. Algebra 22 (1994), 4737–4749. | DOI | MR

[2] H. Chen: Exchange rings with artinian primitive factors. Algebras Represent. Theory 2 (1999), 201–207. | MR | Zbl

[3] H. Chen: Rings with many idempotents. Internat. J.  Math. Math. Sci. 22 (1999), 547–558. | DOI | MR | Zbl

[4] H. Chen: Units, idempotents and stable range conditions. Comm. Algebra 29 (2001), 703–717. | DOI | MR | Zbl

[5] H. Chen: Stable ranges for Morita contexts. SEA  Bull. Math. 25 (2001), 209–216. | DOI | MR | Zbl

[6] K. R. Goodearl and P. Menal: Stable range one for rings with many units. J.  Pure Appl. Algebra 54 (1988), 261–287. | DOI | MR

[7] A. Haghany: Hopficity and co-hopficity for Morita contexts. Comm. Algebra 27 (1999), 477–492. | DOI | MR | Zbl

[8] J. Han and W. K. Nicholson: Extensions of clean rings. Comm. Algebra 29 (2001), 2589–2595. | DOI | MR

[9] M. Henriksen: Two classes of rings generated by their units. J.  Algebra 31 (1974), 182–193. | DOI | MR | Zbl

[10] Y. Hirano: Another triangular matrix ring having Auslander-Gorenstein property. Comm. Algebra 29 (2001), 719–735. | DOI | MR | Zbl

[11] P. Menal: On $\pi $-regular rings whose primitive factor rings are artinian. J.  Pure. Appl. Algebra 20 (1981), 71–78. | DOI | MR | Zbl

[12] W. K. Nicholson: Strongly clean rings and Fitting’s lemma. Comm. Algebra 27 (1999), 3583–3592. | DOI | MR | Zbl

[13] W. K. Nicholson and K. Varadarjan: Countable linear transformations are clean. Proc. Amer. Math. Soc. 126 (1998), 61–64. | DOI | MR

[14] E. Pardo: Comparability, separativity, and exchange rings. Comm. Algebra 24 (1996), 2915–2929. | DOI | MR | Zbl

[15] T. Wu and W. Tong: Stable range condition and cancellation of modules. Pitman Res. Notes Math. 346 (1996), 98–104. | MR

[16] H. P. Yu: On the structure of exchange rings. Comm. Algebra 25 (1997), 661–670. | DOI | MR | Zbl