JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (4): 21-24.doi: 10.6040/j.issn.1671-9352.0.2019.802

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A new generalization of C(P)acts

QIAO Hu-sheng, XU Yang*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2020-04-09

Abstract: Let S be a monoid. A generalization of regular right act is studied, which is called principally weakly C(P)act. A right S-act A is called a principally weakly C(P)act if all cyclic subacts of A satisfy condition(PWP). The characterization of principally weakly P(P)monoids are mainly characterized by principally weakly C(P)properties, the homological classification problem on principally weakly C(P)acts is investigated.

Key words: S-acts, principally weakly C(P)act, principally weakly P(P)monoid

CLC Number: 

  • O152.7
[1] VALDIS L. Pullbacks and flatness properties of acts I[J]. Communications in Algebra, 2001, 29(2):829-850.
[2] 刘仲奎, 乔虎生. 半群的S-系理论[M]. 北京: 科学出版社, 2008. LIU Zhongkui, QIAO Husheng. The S-act theory of semigroups[M]. Beijing: Science Press, 2008.
[3] GOLCHIN A, RENSHAW J. Periodic monoids over which all flat cyclic right acts satisfy condition(P)[J]. Semigroup Forum, 1997, 54:261-263.
[4] LIU Zhongkui. Characterization of monoids by condition(P)of cyclic left acts[J]. Semigroup Forum, 1994, 49(1):31-39.
[5] BARTHIAUME P. The injective envelope of S-acts[J]. Canad Math Bull, 1967, 10:261-273.
[6] 乔虎生. C(P)系对幺半群的刻画[J]. 数学研究与评论, 2004, 24(1):119-126. QIAO Husheng. Characterization of monoids by C(P)acts[J]. Journal of Mathematical Research and Exposition, 2004, 24(1):119-126.
[7] 梁星亮, 吴苏朋, 任军. C(P')系对幺半群的刻画[J]. 山东大学学报(理学报), 2018, 53(10):9-13. LIANG Xingliang, WU Supeng, REN Jun. Characterization of monoids by C(P')acts[J]. Journal of Shandong University(Natural Science), 2018, 53(10):9-13.
[8] KILP M, KNAUER U. Characterization of monoids by properties of regular acts[J]. Journal of Pure and Applied Algebra, 1987, 46:217-231.
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[4] QIAO Hu-sheng, BAI Yong-fa. Characterization of monoids by inverse S-acts [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 1-4.
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