| Title:
|
Regularly weakly based modules over right perfect rings and Dedekind domains (English) |
| Author:
|
Hrbek, Michal |
| Author:
|
Růžička, Pavel |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
367-377 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A weak basis of a module is a generating set of the module minimal with respect to inclusion. A module is said to be regularly weakly based provided that each of its generating sets contains a weak basis. We study \endgraf (1) rings over which all modules are regularly weakly based, refining results of Nashier and Nichols, and \endgraf (2) regularly weakly based modules over Dedekind domains. (English) |
| Keyword:
|
weak basis |
| Keyword:
|
regularly weakly based ring |
| Keyword:
|
Dedekind domain |
| Keyword:
|
perfect ring |
| MSC:
|
13C05 |
| MSC:
|
13F05 |
| MSC:
|
16L30 |
| idZBL:
|
Zbl 06738524 |
| idMR:
|
MR3661046 |
| DOI:
|
10.21136/CMJ.2017.0632-15 |
| . |
| Date available:
|
2017-06-01T14:27:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146761 |
| . |
| Reference:
|
[1] Anderson, F. W., Fuller, K. R.: Rings and Categories of Modules.Graduate Texts in Mathematics 13, Springer, New York (1992). Zbl 0765.16001, MR 1245487, 10.1007/978-1-4612-4418-9 |
| Reference:
|
[2] Berrick, A. J., Keating, M. E.: An Introduction to Rings and Modules with $K$-Theory in View.Cambridge Studies in Advanced Mathematics 65, Cambridge University Press, Cambridge (2000). Zbl 0949.16001, MR 1757884 |
| Reference:
|
[3] Dlab, V.: On a characterization of primary abelian groups of bounded order.J. Lond. Math. Soc. 36 (1961), 139-144. Zbl 0104.02601, MR 0123604, 10.1112/jlms/s1-36.1.139 |
| Reference:
|
[4] Herden, D., Hrbek, M., Růžička, P.: On the existence of weak bases for vector spaces.Linear Algebra Appl. 501 (2016), 98-111. Zbl 1338.15004, MR 3485061, 10.1016/j.laa.2016.03.001 |
| Reference:
|
[5] Hrbek, M., Růžička, P.: Weakly based modules over Dedekind domains.J. Algebra 399 (2014), 251-268. Zbl 1308.13013, MR 3144587, 10.1016/j.jalgebra.2013.09.031 |
| Reference:
|
[6] Hrbek, M., Růžička, P.: Characterization of Abelian groups with a minimal generating set.Quaest. Math. 38 (2015), 103-120. MR 3334638, 10.2989/16073606.2014.981704 |
| Reference:
|
[7] Kaplansky, I.: Infinite Abelian Groups.University of Michigan Publications in Mathematics 2, University of Michigan Press, Ann Arbor (1954). Zbl 0057.01901, MR 0065561 |
| Reference:
|
[8] Krylov, P. A., Tuganbaev, A. A.: Modules over Discrete Valuation Domains.De Gruyter Expositions in Mathematics 43, Walter de Gruyter, Berlin (2008). Zbl 1144.13001, MR 2387130, 10.1515/9783110205787 |
| Reference:
|
[9] Nashier, B., Nichols, W.: A note on perfect rings.Manuscr. Math. 70 (1991), 307-310. Zbl 0721.16009, MR 1089066, 10.1007/BF02568380 |
| Reference:
|
[10] Neggers, J.: Cyclic rings.Rev. Un. Mat. Argentina 28 (1977), 108-114. Zbl 0371.16011, MR 0463238 |
| Reference:
|
[11] Passman, D. S.: A Course in Ring Theory.Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove (1991). Zbl 0783.16001, MR 1096302 |
| . |
