JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (2): 1-7.doi: 10.6040/j.issn.1671-9352.0.2022.489

   

*-zip rings

WANG Yao1, LI Xin1, REN Yanli2*   

  1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China;
    2. School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, Jiangsu, China
  • Published:2024-02-20

Abstract: The concept of *-zip ring is introduced. Some examples of this class rings are given and their extension properties are investigate, prove that(1)Let R be a *-ring, n∈N and n≥2, then R is *-zip if and only if Vn(R)is *^ - zip;(2)Let R be a *-skew Armendariz ring, then R is *-zip if and only if *-skew polynomial ring R[x;*] is *-zip.

Key words: involution, *-zip ring, extension of ring, *-skew polynomial ring

CLC Number: 

  • O153.39
[1] ZELMANOWITZ J M. The finite intersection property on annihilator right ideals[J]. Proceedings of the American Mathematical Society, 1976, 57(2):213-216.
[2] FAITH C. Rings with zero intersection property on annihilators: zip rings[J]. Publicacions Matemátiques, 1989, 33(2):329-338.
[3] FAITH C. Annihilator ideals, associated primes and Kasch-McCoy commutative rings[J]. Communications in Algebra, 1991, 19(7):1967-1982.
[4] HONG C Y, KIM N K, KWAK T K, et al. Extensions of zip rings[J]. Journal of Pure and Applied Algebra, 2005, 195:231-242.
[5] ZIEMBOWSKI M. A note on zip rings[J]. Acta Mathematica Hungarica, 2013, 141:127-131.
[6] CEDÓ F. Zip rings and Malcev domains[J]. Communications in Algebra, 1991, 19(7):1983-1991.
[7] LEROY A, MATCZUK J. Zip property of certain ring extensions[J]. Journal of Pure and Applied Algebra, 2016, 220:335-345.
[8] BERBERIAN S K. Baer *-rings[M]. Berlin: Springer, 1972.
[9] HERSTEIN I N. Rings with involution[M]. Chicago: The University of Chicago Press, 1976.
[10] FAKIEH W M, NAUMAN S K. Reversible rings with involutions and some minimalities[J]. The Scientific World Journal, 2013, 8:1-8.
[11] REGE M B, CHHAWCHHARIA S. Armendariz rings[J]. Proceedings of the Japan Academy Series A Mathematical Sciences, 1997, 73(1):14-17.
[12] FAKIEH W M. *-skew polynomial rings[J]. British Journal of Mathematics & Computer Science, 2015, 10(4):1-12.
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