BibTex RIS Kaynak Göster

QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS

Yıl 2014, , 208 - 217, 01.06.2014
https://doi.org/10.24330/ieja.266248

Öz

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.

Kaynakça

  • 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)
Yıl 2014, , 208 - 217, 01.06.2014
https://doi.org/10.24330/ieja.266248

Öz

Kaynakça

  • 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)
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA59ZA37YG
Bölüm Makaleler
Yazarlar

Tai Keun Kwak Bu kişi benim

Min Jung Lee Bu kişi benim

Yang Lee Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2014
Yayımlandığı Sayı Yıl 2014

Kaynak Göster

APA Kwak, T. K., Lee, M. J., & Lee, Y. (2014). QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS. International Electronic Journal of Algebra, 15(15), 208-217. https://doi.org/10.24330/ieja.266248
AMA Kwak TK, Lee MJ, Lee Y. QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS. IEJA. Haziran 2014;15(15):208-217. doi:10.24330/ieja.266248
Chicago Kwak, Tai Keun, Min Jung Lee, ve Yang Lee. “QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS”. International Electronic Journal of Algebra 15, sy. 15 (Haziran 2014): 208-17. https://doi.org/10.24330/ieja.266248.
EndNote Kwak TK, Lee MJ, Lee Y (01 Haziran 2014) QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS. International Electronic Journal of Algebra 15 15 208–217.
IEEE T. K. Kwak, M. J. Lee, ve Y. Lee, “QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS”, IEJA, c. 15, sy. 15, ss. 208–217, 2014, doi: 10.24330/ieja.266248.
ISNAD Kwak, Tai Keun vd. “QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS”. International Electronic Journal of Algebra 15/15 (Haziran 2014), 208-217. https://doi.org/10.24330/ieja.266248.
JAMA Kwak TK, Lee MJ, Lee Y. QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS. IEJA. 2014;15:208–217.
MLA Kwak, Tai Keun vd. “QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS”. International Electronic Journal of Algebra, c. 15, sy. 15, 2014, ss. 208-17, doi:10.24330/ieja.266248.
Vancouver Kwak TK, Lee MJ, Lee Y. QUASI-ARMENDARIZ PROPERTY ON POWERS OF COEFFICIENTS. IEJA. 2014;15(15):208-17.