Abstract
We characterize prime submodules of R × R for a principal ideal domain R and investigate the primary decomposition of any submodule into primary submodules of R × R.
Similar content being viewed by others
References
J. Jenkins and P. F. Smith: On the prime radical of a module over a commutative ring. Comm. Algebra 20(12) (1992), 3593–3602.
C. P. Lu: Prime submodules of modules. Comm. Math. Univ. Sancti. Pauli 33 (1984), 61–69.
C. P. Lu: M-radicals of submodules in modules. Math. Japon. 34 (1989), no. 2, 211–219.
C. P. Lu: M-radicals of submodules in modules II. Math. Japon. 35 (1990), no. 5, 991–1001.
S. M. George, R. Y. McCasland and P. F. Smith: A principal ideal theorem analogue for modules over commutative rings. Comm. Algebra 22(6) (1994), 2083–2099.
R. Y. McCasland and M. E. Moore: On radicals of submodules of finitely generated modules. Canad. Math. Bull. 29(1) (1986).
R. Y. McCasland and P. F. Smith: Prime submodules of Noetherian modules. Rocky Mountain J. Math. 23 (1993), no. 3.
H. Matsumura: Commutative Ring Theory. Cambridge University Press, 1980.
R. Y. Sharp: Steps in Commutative Algebra. Cambridge University Press, 1990.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tiras, Y., Harmanci, A. On prime submodules and primary decomposition. Czechoslovak Mathematical Journal 50, 83–90 (2000). https://doi.org/10.1023/A:1022441220553
Issue Date:
DOI: https://doi.org/10.1023/A:1022441220553