| Title:
|
On strongly $(P)$-cyclic acts (English) |
| Author:
|
Golchin, Akbar |
| Author:
|
Rezaei, Parisa |
| Author:
|
Mohammadzadeh, Hossein |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
595-611 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong $(P)$-cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts. (English) |
| Keyword:
|
strongly $(P)$-cyclic |
| Keyword:
|
right $PCP$ |
| Keyword:
|
Rees factor act |
| MSC:
|
20M30 |
| idZBL:
|
Zbl 1207.20062 |
| idMR:
|
MR2545643 |
| . |
| Date available:
|
2010-07-20T15:28:11Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140503 |
| . |
| Reference:
|
[1] Howie, J. M.: Fundamentals of Semigroup Theory.London Mathematical Society Monographs, OUP (1995). Zbl 0835.20077, MR 1455373 |
| Reference:
|
[2] Kilp, M.: Characterization of monoids by properties of their left Rees factors.Tartu Ül. Toimetised 640 (1983), 29-37. MR 0706740 |
| Reference:
|
[3] Kilp, M., Knauer, U., Mikhalev, A.: Monoids, Acts and Categories: With Applications to Wreath Products and Graphs: A Handbook for Students and Researchers.Walter de Gruyter, Berlin (2000). Zbl 0945.20036, MR 1751666 |
| Reference:
|
[4] Laan, V.: Pullbacks and flatness properties of acts.PhD Thesis, Tartu (1999). Zbl 1011.20500, MR 1720086 |
| Reference:
|
[5] Laan, V.: Pullbacks and flatness properties of acts I.Comm. Algebra 29 (2001), 829-850. Zbl 0987.20047, MR 1842004, 10.1081/AGB-100001547 |
| Reference:
|
[6] Normak, P.: Analogies of QF-ring for monoids. I.Tartu Ül. Toimetised 556 (1981), 38-46. MR 0630693 |
| Reference:
|
[7] Tran, L. H.: Characterizations of monoids by regular acts.Period. Math. Hung. 16 (1985), 273-279. MR 0833262, 10.1007/BF01848077 |
| . |
