JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 1-5, 12.doi: 10.6040/j.issn.1671-9352.0.2022.457

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Condition (P) and strong flatness

Xinyi WU(),Husheng QIAO*()   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-09-07 Online:2024-06-20 Published:2024-06-17
  • Contact: Husheng QIAO E-mail:1404629418@qq.com;gsqiaohsh@163.com

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Abstract:

Let S be a monoid, A be a right S-act. The monoids over which all right S-acts satisfying Condition (P) are strongly flat are studied. Some new classes of monoids are obtained, and the derivation relationship between them is proven. The existing results are generalized.

Key words: Condition (P), Condition (E), strong flatness

CLC Number: 

  • O152.7
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3 QIAO Husheng . Strong flatness properties of right S-acts satisfying Condition (P)[J]. Communications in Algebra, 2002, 30 (9): 4321- 4330.
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4 QIAO Husheng , LI Lian . Some conditions on monoids for which Condition(P) acts are strongly flat[J]. Communications in Algebra, 2004, 32 (12): 4795- 4330.
doi: 10.1081/AGB-200039282
5 QIAO Husheng , LI Fang . On monoids for which Condition(P) acts are strongly flat[J]. Communications in Algebra, 2009, 37 (1): 234- 241.
doi: 10.1080/00927870802243671
[1] ZHAO Mei-mei, QIAO Hu-sheng*. On a generalization of (P)-covers of cyclic acts [J]. J4, 2012, 47(4): 94-96.
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