REVERSIBILITY OVER UPPER NILRADICALS |
Jung, Da Woon
(Finance Fishery Manufacture Industrial Mathematics Center on Big Data Pusan National University)
Lee, Chang Ik (Department of Mathematics Pusan National University) Piao, Zhelin (Department of Mathematics Yanbian University) Ryu, Sung Ju (Department of Mathematics Pusan National University) Sung, Hyo Jin (Department of Mathematics Pusan National University) Yun, Sang Jo (Department of Mathematics Dong-A University) |
1 | T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, 131, Springer-Verlag, New York, 1991. https://doi.org/10.1007/978-1-4684-0406-7 |
2 | L. Liang, L.Wang, and Z. Liu, On a generalization of semicommutative rings, Taiwanese J. Math. 11 (2007), no. 5, 1359-1368. https://doi.org/10.11650/twjm/1500404869 DOI |
3 | G. Marks, On 2-primal Ore extensions, Comm. Algebra 29 (2001), no. 5, 2113-2123. https://doi.org/10.1081/AGB-100002173 DOI |
4 | L. Motais de Narbonne, Anneaux semi-commutatifs et uniseriels; anneaux dont les ideaux principaux sont idempotents, in Proceedings of the 106th National Congress of Learned Societies (Perpignan, 1981), 71-73, Bib. Nat., Paris. |
5 | M. B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 1, 14-17. http://projecteuclid.org/euclid.pja/1195510144 DOI |
6 | L. H. Rowen, Ring Theory, student edition, Academic Press, Inc., Boston, MA, 1991. |
7 | 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 DOI |
8 | D. D. Anderson and V. Camillo, Semigroups and rings whose zero products commute, Comm. Algebra 27 (1999), no. 6, 2847-2852. https://doi.org/10.1080/00927879908826596 DOI |
9 | 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 DOI |
10 | E. P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Austral. Math. Soc. 18 (1974), 470-473. DOI |
11 | G. F. Birkenmeier, H. E. Heatherly, and E. K. Lee, Completely prime ideals and associated radicals, in Ring theory (Granville, OH, 1992), 102-129, World Sci. Publ., River Edge, NJ, 1993. |
12 | W. Chen, On nil-semicommutative rings, Thai J. Math. 9 (2011), no. 1, 39-47. |
13 | Y. Hirano, D. van Huynh, and J. K. Park, On rings whose prime radical contains all nilpotent elements of index two, Arch. Math. (Basel) 66 (1996), no. 5, 360-365. https://doi.org/10.1007/BF01781553 DOI |
14 | P. M. Cohn, Reversible rings, Bull. London Math. Soc. 31 (1999), no. 6, 641-648. https://doi.org/10.1112/S0024609399006116 DOI |
15 | N. Divinsky, Rings and Radicals, Mathematical Expositions No. 14, University of Toronto Press, Toronto, ON, 1965. |
16 | 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 DOI |
17 | C. Huh, H. K. Kim, and Y. Lee, p.p. rings and generalized p.p. rings, J. Pure Appl. Algebra 167 (2002), no. 1, 37-52. https://doi.org/10.1016/S0022-4049(01)00149-9 DOI |
18 | 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 DOI |
19 | S. U. Hwang, Y. C. Jeon, and K. S. Park, On NCI rings, Bull. Korean Math. Soc. 44 (2007), no. 2, 215-223. https://doi.org/10.4134/BKMS.2007.44.2.215 DOI |
20 | D. W. Jung, Y. Lee, and H. J. Sung, Reversibility over prime radicals, Korean J. Math. 22 (2014), 279-288. http://doi.org/10.11568/kjm.2014.22.2.279 DOI |
21 | N. K. Kim, K. H. Lee, and Y. Lee, Power series rings satisfying a zero divisor property, Comm. Algebra 34 (2006), no. 6, 2205-2218. https://doi.org/10.1080/00927870600549782 DOI |
22 | 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 DOI |
23 | G. Kothe, Die Struktur der Ringe, deren Restklassenring nach dem Radikal vollstandig reduzibel ist, Math. Z. 32 (1930), no. 1, 161-186. https://doi.org/10.1007/BF01194626 DOI |