JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (10): 6-10.doi: 10.6040/j.issn.1671-9352.0.2021.694

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On the characterizations of P-principally weakly injective acts

QIAO Hu-sheng, YUAN Ying-min*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2022-10-06

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Abstract: Let S be a monoid and P be a nonempty subset of S. A new kind of principally weakly injective act is defined, which is based on the embedding principal right ideals generated by elements in P and is called P-principally weakly injective act. Using this new property, the characterizations of some new classes of monoids are given.

Key words: S-act, P-principally weakly injective, principally weakly injective

CLC Number: 

  • O152.7
[1] 乔虎生, 刘仲奎. 半群引论[M]. 北京: 科学出版社, 2019. QIAO Husheng, LIU Zhongkui. An introduction to semigroups[M]. Beijing: Science Press, 2019.
[2] KILP M, KNAUER U, MIKHALEV A V. Monoids, acts and categories[M] //De Gruyter Expositions in Mathematics, 29. Berlin: De Gruyter Mouton, 2000.
[3] QIAO Husheng, YIN Haiyan. On a new kind of principally weakly injective acts over monoids[J]. Journal of Lanzhou University(Natural Sciences), 2013, 49(5):715-718.
[4] 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.
[5] GOULD V. Divisiable S-systems and R-modules[J]. Proceedings Edinburgh Mathematics Society, 1987, 30(2):187-200.
[6] ZHANG Xia, KNAUER U, CHEN Yuqun. Various notions of weak injectivity over Clifford semigroups[J]. Semigroups Forum, 2008, 76(2):357-367.
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