Quasipolar matrix rings over local rings
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
A ring R is called quasipolar if for every a 2 R there exists p2 = p ∈ R such that p ∈ comm2 R(a), a + p ∈ U(R) and ap 2∈Rqnil. The class of quasipolar rings lies properly between the class of strongly π-regular rings and the class of strongly clean rings. In this paper, we determine when a 2 × 2 matrix over a local ring is quasipolar. Necessary and sufficient conditions for a 2 × 2 matrix ring to be quasipolar are obtained.
Abstract
A ring R is called quasipolar if for every a 2 R there exists p2 = p ∈ R such that p ∈ comm2 R(a), a + p ∈ U(R) and ap 2∈Rqnil. The class of quasipolar rings lies properly between the class of strongly π-regular rings and the class of strongly clean rings. In this paper, we determine when a 2 × 2 matrix over a local ring is quasipolar. Necessary and sufficient conditions for a 2 × 2 matrix ring to be quasipolar are obtained.
참고문헌 (18)
- G. Borooah, "Strongly clean triangular matrix rings over local rings", J. Algebra, 312(2), pp.773~797 (2007)
- G. Borooah, "Strongly clean matrix rings over commutative local rings", J. Pure Appl. Algebra, 212(1), pp.281~296 (2008)
- J. Chen, "When is the 2×2 matrix ring over a commutative local ring strongly clean?", J. Algebra, 301(1), pp.280~293 (2006)
- J. Chen, "On strongly clean matrix and triangular matrix rings", Comm. Algebra, 34(10), pp.3659~3674 (2006)
- P. M. Cohn, "Free Rings and Their Relations" (1985), Academic Press
- J. Cui, "When is a 2×2 matrix ring over a commutative local ring quasipo-lar?", Comm. Algebra, 39(9), pp.3212~3221 (2011)
- J. Cui, "Characterizations of quasipolar rings", Comm. Algebra, 41(9), pp.3207~3217 (2013)
- M. F. Dischinger, "Sur les anneaux fortement -r´eguliers", C. R. Math. Acad. Sci. Paris, 283(8), pp.571~573 (1976)
- J. Han, "Extensions of clean rings", Comm. Algebra, 29(6), pp.2589~2595 (2001)
- R. E. Harte, "On quasinilpotents in rings", Panam. Math. J, 1, pp.10~16 (1991)
- J. J. Koliha, "Elements of rings with equal spectral idempotents", J. Aust. Math. Soc, 72(1), pp.137~152 (2002)
- Li Bingjun, "Strongly clean matrix rings over noncommutative local rings", 대한수학회보, 46(1), pp.71~78 (2009), 대한수학회
- Y. Li, "Strongly clean matrix rings over local rings", J. Algebra, 312(1), pp.397~404 (2007)
- W. K. Nicholson, "Local group rings", Canad. Math. Bull, 15, pp.137~138 (1972)
- W. K. Nicholson, "Strongly clean rings and Fitting’s lemma", Comm. Algebra, 27(8), pp.3583~3592 (1999)
- Z. Wang, "On two open problems about strongly clean rings", Bull. Aust. Math. Soc, 70(2), pp.279~282 (2004)
- X. Yang, "Strong cleanness of the 2 × 2 matrix ring over a general local ring", J. Algebra, 320(6), pp.2280~2290 (2008)
- Z. Ying, "On quasipolar rings", Algebra Colloq, 19(4), pp.683~692 (2012)