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http://dx.doi.org/10.11568/kjm.2015.23.3.337

ON A RING PROPERTY GENERALIZING POWER-ARMENDARIZ AND CENTRAL ARMENDARIZ RINGS  

CHA, HO JUN (Department of Mathematics Pusan National University)
JUNG, DA WOON (Department of Mathematics Pusan National University)
KIM, HONG KEE (Department of Mathematics and RINS Gyeongsang National University)
KIM, JIN-A (Department of Mathematics Pusan National University)
LEE, CHANG IK (Department of Mathematics Pusan National University)
LEE, YANG (Department of Mathematics Pusan National University)
NAM, SANG BOK (Department of Early Child Education Kyungdong University)
RYU, SUNG JU (Department of Mathematics Pusan National University)
SEO, YEONSOOK (Department of Mathematics Pusan National University)
SUNG, HYO JIN (Department of Mathematics Pusan National University)
YUN, SANG JO (Department of Mathematics Pusan National University)
Publication Information
Korean Journal of Mathematics / v.23, no.3, 2015 , pp. 337-355 More about this Journal
Abstract
We in this note consider a class of rings which is related to both power-Armendariz and central Armendariz rings, in the spirit of Armendariz and Kaplansky. We introduce central power-Armendariz as a generalization of them, and study the structure of central products of coefficients of zero-dividing polynomials. We also observe various sorts of examples to illuminate the relations between central power-Armendariz and related ring properties.
Keywords
central power-Armendariz ring; Armendariz ring; central products of coefficients; K-ring;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 N. Agayev, G. Gungoroglu, A. Harmanci, S. Halicioglu, Central Armendariz rings, Bull. Malays. Math. Sci. Soc. 34 (2011), 137-145.
2 N. Agayev, T. Ozen, A. Harmanci, On a Class of semicommutative rings, Kyungpook Math. J. 51 (2011), 283-291.   DOI   ScienceOn
3 D.D. Anderson, V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra 26 (1998), 2265-2272.   DOI   ScienceOn
4 R. Antoine, Nilpotent elements and Armendariz rings, J. Algebra 319 (2008), 3128-3140.   DOI   ScienceOn
5 E.P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Austral. Math. Soc. 18 (1974), 470-473.   DOI
6 H.E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2 (1970), 363-368.   DOI
7 G.M. Bergman, Coproducts and some universal ring constructions, Tran. Amer. Math. Soc. 200 (1974), 33-88.   DOI
8 G.M. Bergman, Modules over coproducts of rings, Trans. Amer. Math. Soc. 200 (1974), 1-32.   DOI
9 G.F. Birkenmeier, J.Y. Kim and J.K. Park, Principally quasi-Baer rings, Comm. Algebra 29 (2001), 470-473.
10 W.E. Clark, Twisted matrix units semigroup algebras, Duke. Math. J. 34 (1967), 417-423.   DOI
11 K.R. Goodearl, Von Neumann Regular Rings, Pitman, London (1979).
12 K.R. Goodearl, R.B. Warfield, JR., An Introduction to Noncommutative Noetherian Rings, Cambridge University Press, Cambridge-New York-Port Chester-Melbourne-Sydney (1989).
13 J. Han, T.K. Kwak, C.I. Lee, Y. Lee, Y. Seo, Ring properties in relation to powers, (submitted).
14 I. N. Herstein, A theorem on rings, Canad. J. Math. 5 (1953), 238-241.   DOI
15 C. Huh, Y. Lee, A note on ${\pi}$-regular rings, Kyungpook Math. J. 38 (1998), 157-161.
16 C. Huh, Y. Lee, A. Smoktunowicz, Armendariz rings and semicommutative ring, Comm. Algebra 30 (2002), 751-761.   DOI   ScienceOn
17 D.W. Jung, N.K. Kim, Y. Lee, S.P. Yang, Nil-Armendariz rings and upper nilradicals, Internat. J. Math. Comput. 22 (2012), 1250059 (1-13).
18 I. Kaplansky, A theorem on division rings, Canad. J. Math. 3 (1951), 290-292.   DOI
19 I. Kaplansky, Rings of Operators, W.A. Benjamin, Inc., New York, 1968.
20 N.K. Kim, K.H. Lee and Y. Lee, Power series rings satisfying a zero divisor property, Comm. Algebra 34 (2006), 2205-2218.   DOI   ScienceOn
21 N.K. Kim, Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), 477-488.   DOI   ScienceOn
22 N.K. Kim, Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra 185 (2003), 207-223.   DOI   ScienceOn
23 T.K. Kwak, Y. Lee, Rings over which coe${\delta}$cients of nilpotent polynomials are nilpotent, Internat. J. Algebra Comput. 21 (2011), 745-762.   DOI   ScienceOn
24 N. Jacobson, Structure of Rings, American Mathematical Society Colloquium Publications, Vol. 37. Revised edition American Mathematical Society, Providence, R.I. 1964.
25 D.W. Jung, N.K. Kim, Y. Lee, S.P. Yang, Properties of K-rings and rings satisfying similar conditions, Internat. J. Math. Comput. 21 (2011), 1381-1394.
26 Z. Liu, R. Zhao, On Weak Armendariz Rings, Comm. Algebra 34 (2006), 2607-2616.   DOI   ScienceOn
27 M.B. Rege, S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), 14-17.   DOI