journal6 ›› 2013, Vol. 34 ›› Issue (1): 1-5.DOI: 10.3969/j.issn.1007-2985.2013.01.001

• Mathematics •     Next Articles

Zero-Divisor Rings and Related Rings


  1. (1.School of Mathematics and Information Technology,Nanjing Xiaozhuang University,Nanjing 211171,China;2.School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)
  • Online:2013-01-25 Published:2013-01-22
  • About author:REN Yan-li(1965-),female,was born in Keshan,Heilongjiang Province,professor of Nanjing Xiaozhuang University,M.S.D.;research aresa are associative ring and associative algebra.
  • Supported by:

    National Natural Science Foundation of China (11071097;11101217);Natural Science Foundation of the Education Department of Jiangsu  Province (11KJB110007)

Abstract: The authors  introduce the concepts of left (right) zero-divisor rings,a class of rings without identity.A ring R is called left (right) zero-divisor if rR(a)≠0(lR(a)≠0) for every a∈R.The authors  investigate the relations between left (right) zero-divisor rings and related rings,and give equivalent characterizations of left zero-divisor rings.

Key words: zero-divisor, left zero-divisor ring, reversible ring, symmetric ring, semicommutative ring, p.p.-ring, Armendariz ring

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