Regularly weakly based modules over right perfect rings and Dedekind domains
Czechoslovak Mathematical Journal (2017)
- Volume: 67, Issue: 2, page 367-377
- ISSN: 0011-4642
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topHrbek, Michal, and Růžička, Pavel. "Regularly weakly based modules over right perfect rings and Dedekind domains." Czechoslovak Mathematical Journal 67.2 (2017): 367-377. <http://eudml.org/doc/288203>.
@article{Hrbek2017,
abstract = {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.},
author = {Hrbek, Michal, Růžička, Pavel},
journal = {Czechoslovak Mathematical Journal},
language = {eng},
number = {2},
pages = {367-377},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regularly weakly based modules over right perfect rings and Dedekind domains},
url = {http://eudml.org/doc/288203},
volume = {67},
year = {2017},
}
TY - JOUR
AU - Hrbek, Michal
AU - Růžička, Pavel
TI - Regularly weakly based modules over right perfect rings and Dedekind domains
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 2
SP - 367
EP - 377
AB - 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.
LA - eng
UR - http://eudml.org/doc/288203
ER -
References
top- Anderson, F. W., Fuller, K. R., 10.1007/978-1-4612-4418-9, Graduate Texts in Mathematics 13, Springer, New York (1992). (1992) Zbl0765.16001MR1245487DOI10.1007/978-1-4612-4418-9
- 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). (2000) Zbl0949.16001MR1757884
- Dlab, V., 10.1112/jlms/s1-36.1.139, J. Lond. Math. Soc. 36 (1961), 139-144. (1961) Zbl0104.02601MR0123604DOI10.1112/jlms/s1-36.1.139
- Herden, D., Hrbek, M., Růžička, P., 10.1016/j.laa.2016.03.001, Linear Algebra Appl. 501 (2016), 98-111. (2016) Zbl1338.15004MR3485061DOI10.1016/j.laa.2016.03.001
- Hrbek, M., Růžička, P., 10.1016/j.jalgebra.2013.09.031, J. Algebra 399 (2014), 251-268. (2014) Zbl1308.13013MR3144587DOI10.1016/j.jalgebra.2013.09.031
- Hrbek, M., Růžička, P., 10.2989/16073606.2014.981704, Quaest. Math. 38 (2015), 103-120. (2015) MR3334638DOI10.2989/16073606.2014.981704
- Kaplansky, I., Infinite Abelian Groups, University of Michigan Publications in Mathematics 2, University of Michigan Press, Ann Arbor (1954). (1954) Zbl0057.01901MR0065561
- Krylov, P. A., Tuganbaev, A. A., 10.1515/9783110205787, De Gruyter Expositions in Mathematics 43, Walter de Gruyter, Berlin (2008). (2008) Zbl1144.13001MR2387130DOI10.1515/9783110205787
- Nashier, B., Nichols, W., 10.1007/BF02568380, Manuscr. Math. 70 (1991), 307-310. (1991) Zbl0721.16009MR1089066DOI10.1007/BF02568380
- Neggers, J., Cyclic rings, Rev. Un. Mat. Argentina 28 (1977), 108-114. (1977) Zbl0371.16011MR0463238
- Passman, D. S., A Course in Ring Theory, Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove (1991). (1991) Zbl0783.16001MR1096302
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