- Volume 33 Issue 3
DOI QR Code
A GENERALIZATION OF ARMENDARIZ AND NI PROPERTIES
- Li, Dan (Department of Mathematics Pusan National University) ;
- Piao, Zhelin (Department of Mathematics Yanbian University) ;
- Yun, Sang Jo (Department of Mathematics Dong-A University)
- Received : 2017.07.11
- Accepted : 2017.09.21
- Published : 2018.07.31
Antoine showed that the properties of Armendariz and NI are independent of each other. The study of Armendariz and NI rings has been doing important roles in the research of zero-divisors in noncommutative ring theory. In this article we concern a new class of rings which generalizes both Armendariz and NI rings. The structure of such sort of ring is investigated in relation with near concepts and ordinary ring extensions. Necessary examples are examined in the procedure.
Supported by : National Research Foundation of Korea(NRF)
- D. D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), no. 7, 2265-2272. https://doi.org/10.1080/00927879808826274
- R. Antoine, Nilpotent elements and Armendariz rings, J. Algebra 319 (2008), no. 8, 3128-3140. https://doi.org/10.1016/j.jalgebra.2008.01.019
- E. P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Austral. Math. Soc. 18 (1974), 470-473. https://doi.org/10.1017/S1446788700029190
- G. F. Birkenmeier, H. E. Heatherly, and E. K. Lee, Completely prime ideals and asso- ciated radicals, in Ring theory (Granville, OH, 1992), 102-129, World Sci. Publ., River Edge, NJ, 1993.
- J. L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38 (1932), no. 2, 85-88. https://doi.org/10.1090/S0002-9904-1932-05333-2
- K. R. Goodearl, von Neumann Regular Rings, Monographs and Studies in Mathematics, 4, Pitman (Advanced Publishing Program), Boston, MA, 1979.
- C. Huh, Y. Lee, and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), no. 2, 751-761. https://doi.org/10.1081/AGB-120013179
- S. U. Hwang, Y. C. Jeon, and Y. Lee, Structure and topological conditions of NI rings, J. Algebra 302 (2006), no. 1, 186-199. https://doi.org/10.1016/j.jalgebra.2006.02.032
- N. K. Kim and Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), no. 2, 477-488. https://doi.org/10.1006/jabr.1999.8017
- G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113-2123. https://doi.org/10.1081/AGB-100002173
- M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14-17. https://doi.org/10.3792/pjaa.73.14
- A. Smoktunowicz, Polynomial rings over nil rings need not be nil, J. Algebra 233 (2000), no. 2, 427-436. https://doi.org/10.1006/jabr.2000.8451