Characterizations of 0-submodules
DOI:
https://doi.org/10.22199/S07160917.1997.0001.00002Keywords:
Prime submodules, 0- submodules, Torsion- free modules, Local cohomologyAbstract
In this paper we give an introduction to prime submodules in order to generalize the concept of prime ideal to the category of modules. First of all, we study prime submodules of ideal 0 in the case where the ring is an integral domain. For this reason we ha ve called these submodules 0 submodules. We show several properties of these submodules are torsion free. This result allows us to apply local cohomology to characterize 0- submodules of rank one of reflexive modules over the polynomial ring in n variables as free modules. Second, we develop two theorems which define a bijection between objects.
References
[2] Eisenbud. D., Commutative Algebra with a View Toward Algebraic Geometry. Springer-Verlag, New York. ( 1995).
[3] Hartsborne, R. Stable Reflexive Sheaves. Mathematische Annalen, 254.. pp. 121-116. (1980).
[4] Kunz, E., lntroduction to Commutative Algebra and Algebraic Geometry. Birkhäuser. Boston. ( 1985).
[5] Matsumura. H .. Commutative Algebra. Benjamin. (1970).
Published
How to Cite
Issue
Section
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
