Yıl 2014, Cilt 15, Sayı 15, Sayfalar 208 - 217 2014-06-01

QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS

Tai Keun Kwak [1] , Min Jung Lee [2] , Yang Lee [3]

158 176

The study of Armendariz rings was initiated by Rege and Chhawchharia, based on a result of Armendariz related to the structure of reduced rings. Armendariz rings were generalized to quasi-Armendariz rings by Hirano. We introduce the concept of power-quasi-Armendariz (simply, p.q.- Armendariz) ring as a generalization of quasi-Armendariz, applying the role of quasi-Armendariz on the powers of coefficients of zero-dividing polynomials. In the process we investigate the power-quasi-Armendariz property of several ring extensions, e.g., matrix rings and polynomial rings, which have roles in ring theory.
power-quasi-Armendariz ring, power of coefficient, quasi-Armendariz ring, Armendariz ring, polynomial ring, matrix ring
  • D.D. Anderson and V. Camillo, Armendariz rings and Gaussian rings, Comm. Algebra, 26 (1998), 2265-2272.
  • E.P. Armendariz, A note on extensions of Baer and P.P.-rings, J. Aust. Math. Soc., 18 (1974), 470-473.
  • M. Ba¸ser, F. Kaynarca, T.K. Kwak and Y. Lee, Weak quasi-Armendariz rings, Algebra Colloq., 18 (2011), 541-552.
  • H.E. Bell, Near-rings in which each element is a power of itself, Bull. Aust. Math. Soc., 2 (1970), 363-368.
  • K.R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.
  • J.C. Han, T.K. Kwak, M.J. Lee, Y. Lee and Y.S. Seo, On powers of coefficients of zero-dividing polynomials, submitted. Y. Hirano, On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra, 168 (2002), 45-52.
  • C. Huh, Y. Lee and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra, 30 (2002), 751-761.
  • D.W. Jung, T.K. Kwak, M.J. Lee and Y. Lee, Ring properties related to sym- metric rings, submitted. N.K. Kim and Y. Lee, Armendariz rings and reduced rings, J. Algebra, 223 (2000), 477–488.
  • N.K. Kim and Y.Lee, Extension of reversible rings, J. Pure Appl. Algebra, 185 (2003), 207-223.
  • T.K. Kwak, Y. Lee and S.J. Yun, The Armendariz property on ideals, J. Alge- bra, 354 (2012), 121-135.
  • J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull., 14 (1971), 359-368.
  • J.C. Shepherdson, Inverses and zero-divisors in matrix ring, Proc. London Math. Soc., 3 (1951), 71-85.
  • M.B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci., 73 (1997), 14-17.
  • G. Shin, Prime ideals and sheaf representation of a pseudo symmetric ring, Trans. Amer. Math. Soc., 184 (1973), 43-60. Tai Keun Kwak
  • Department of Mathematics Daejin University Pocheon 487-711, Korea e-mail: tkkwak@daejin.ac.kr Min Jung Lee and Yang Lee Department of Mathematics Education Pusan National University Pusan 609-735, Korea e-mails: nice1mj@nate.com (Min Jung Lee) ylee@pusan.ac.kr (Yang Lee)
Konular
Diğer ID JA59ZA37YG
Dergi Bölümü Makaleler
Yazarlar

Yazar: Tai Keun Kwak

Yazar: Min Jung Lee

Yazar: Yang Lee

Bibtex @ { ieja266248, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2014}, volume = {15}, pages = {208 - 217}, doi = {10.24330/ieja.266248}, title = {QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS}, key = {cite}, author = {Lee, Yang and Kwak, Tai Keun and Lee, Min Jung} }
APA Kwak, T , Lee, M , Lee, Y . (2014). QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS. International Electronic Journal of Algebra, 15 (15), 208-217. DOI: 10.24330/ieja.266248
MLA Kwak, T , Lee, M , Lee, Y . "QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS". International Electronic Journal of Algebra 15 (2014): 208-217 <http://dergipark.gov.tr/ieja/issue/25196/266248>
Chicago Kwak, T , Lee, M , Lee, Y . "QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS". International Electronic Journal of Algebra 15 (2014): 208-217
RIS TY - JOUR T1 - QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS AU - Tai Keun Kwak , Min Jung Lee , Yang Lee Y1 - 2014 PY - 2014 N1 - doi: 10.24330/ieja.266248 DO - 10.24330/ieja.266248 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 208 EP - 217 VL - 15 IS - 15 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266248 UR - http://dx.doi.org/10.24330/ieja.266248 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS %A Tai Keun Kwak , Min Jung Lee , Yang Lee %T QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS %D 2014 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 15 %N 15 %R doi: 10.24330/ieja.266248 %U 10.24330/ieja.266248
ISNAD Kwak, Tai Keun , Lee, Min Jung , Lee, Yang . "QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS". International Electronic Journal of Algebra 15 / 15 (Haziran 2014): 208-217. http://dx.doi.org/10.24330/ieja.266248