EXTENSIONS OF STRONGLY π-REGULAR RINGS

Title & Authors
EXTENSIONS OF STRONGLY π-REGULAR RINGS
Chen, Huanyin; Kose, Handan; Kurtulmaz, Yosum;

Abstract
An ideal I of a ring R is strongly $\small{{\pi}}$-regular if for any $\small{x{\in}I}$ there exist $\small{n{\in}\mathbb{N}}$ and $\small{y{\in}I}$ such that $x^n Keywords strongly $\small{{\pi}}$-regular ideal;B-ideal;periodic ideal; Language English Cited by References 1. P. Ara, Strongly${\pi}$-regular rings have stable range one, Proc. Amer. Math. Soc. 124 (1996), no. 11, 3293-3298. 2. A. Badawi, A. Y. M. Chin, and H. V. Chen, On rings with near idempotent elements, Internat. J. Pure Appl. Math. 1 (2002), no. 3, 253-259. 3. 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. 4. M. Chacron, On a theorem of Herstein, Canad. J. Math. 21 (1969), 1348-1353. 5. H. Chen, Rings Related to Stable Range Conditions, Series in Algebra 11, World Scientific, Hackensack, NJ, 2011. 6. H. Chen and M. Chen, On strongly${\pi}$-regular ideals, J. Pure Appl. Algebra 195 (2005), no. 1, 21-32. 7. A. J. Diesl and T. J. Dorsey, A note on completeness in the theory of strongly clean rings, Preprint. 8. X. Du and Y. Yang, The adjoint semigroup of a${\pi}$-regular rings, Acta Sci. Natur. Univ. Jilin. 3 (2001), no. 3, 35-37. 9. K. R. Goodearl, Von Neumann Regular Rings, Pitman, London, San Francisco, Melbourne, 1979. 10. N. K. Kim and Y. Lee, On strong${\pi}$-regularity and${\pi}$-regularity, Comm. Algebra 39 (2011), no. 11, 4470-4485. 11. M. Ohori, On strongly${\pi}$-regular rings and periodic rings, Math. J. Okayama Univ. 27 (1985), 49-52. 12. F. T. Shirley, Regular and Strongly II-Regular Rings, University of Texas at Austin, 1984. 13. L.W.White, Strongly II-Regular Rings and Matrix Rings over Regular Rings, University of Texas at Austin, 1987. 14. H. P. Yu, On strongly${\pi}\$-regular rings of stable range one, Bull. Austral. Math. Soc. 51 (1995), no. 3, 433-437.