QUASIPOLAR MATRIX RINGS OVER LOCAL RINGS

Title & Authors
QUASIPOLAR MATRIX RINGS OVER LOCAL RINGS
Cui, Jian; Yin, Xiaobin;

Abstract
A ring R is called quasipolar if for every a 2 R there exists $p^2 Keywords quasipolar ring;matrix ring;strongly clean ring;local ring; Language English Cited by References 1. G. Borooah, A. J. Diesl, and T. J. Dorsey, Strongly clean triangular matrix rings over local rings, J. Algebra 312 (2007), no. 2, 773-797. 2. G. Borooah, A. J. Diesl, and T. J. Dorsey, Strongly clean matrix rings over commutative local rings, J. Pure Appl. Algebra 212 (2008), no. 1, 281-296. 3. J. Chen, X. Yang, and Y. Zhou, When is the$2{\times}2$matrix ring over a commutative local ring strongly clean?, J. Algebra 301 (2006), no. 1, 280-293. 4. J. Chen, X. Yang, and Y. Zhou, On strongly clean matrix and triangular matrix rings, Comm. Algebra 34 (2006), no. 10, 3659-3674. 5. P. M. Cohn, Free Rings and Their Relations, 2nd edn, Academic Press, 1985. 6. J. Cui and J. Chen, When is a$2{\times}2$matrix ring over a commutative local ring quasipo- lar?, Comm. Algebra 39 (2011), no. 9, 3212-3221. 7. J. Cui and J. Chen, Characterizations of quasipolar rings, Comm. Algebra 41 (2013), no. 9, 3207- 3217. 8. M. F. Dischinger, Sur les anneaux fortement${\pi}$-reguliers, C. R. Math. Acad. Sci. Paris 283 (1976), no. 8, 571-573. 9. J. Han and W. K. Nicholson, Extensions of clean rings, Comm. Algebra 29 (2001), no. 6, 2589-2595. 10. R. E. Harte, On quasinilpotents in rings, Panam. Math. J. 1 (1991), 10-16. 11. J. J. Koliha and P. Patricio, Elements of rings with equal spectral idempotents, J. Aust. Math. Soc. 72 (2002), no. 1, 137-152. 12. B. Li, Strongly clean matrix rings over noncommutative local rings, Bull. korean Math. Soc. 46 (2009), no. 1, 71-78. 13. Y. Li, Strongly clean matrix rings over local rings, J. Algebra 312 (2007), no. 1, 397-404. 14. W. K. Nicholson, Local group rings, Canad. Math. Bull. 15 (1972), 137-138. 15. W. K. Nicholson, Strongly clean rings and Fitting's lemma, Comm. Algebra 27 (1999), no. 8, 3583-3592. 16. Z. Wang and J. Chen, On two open problems about strongly clean rings, Bull. Aust. Math. Soc. 70 (2004), no. 2, 279-282. 17. X. Yang and Y. Zhou, Strong cleanness of the$2{\times}2\$ matrix ring over a general local ring, J. Algebra 320 (2008), no. 6, 2280-2290.

18.
Z. Ying and J. Chen, On quasipolar rings, Algebra Colloq. 19 (2012), no. 4, 683-692.