Skip to main content
Log in

On prime submodules and primary decomposition

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Jenkins and P. F. Smith: On the prime radical of a module over a commutative ring. Comm. Algebra 20(12) (1992), 3593–3602.

    Google Scholar 

  2. C. P. Lu: Prime submodules of modules. Comm. Math. Univ. Sancti. Pauli 33 (1984), 61–69.

    Google Scholar 

  3. C. P. Lu: M-radicals of submodules in modules. Math. Japon. 34 (1989), no. 2, 211–219.

    Google Scholar 

  4. C. P. Lu: M-radicals of submodules in modules II. Math. Japon. 35 (1990), no. 5, 991–1001.

    Google Scholar 

  5. 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.

    Google Scholar 

  6. R. Y. McCasland and M. E. Moore: On radicals of submodules of finitely generated modules. Canad. Math. Bull. 29(1) (1986).

  7. R. Y. McCasland and P. F. Smith: Prime submodules of Noetherian modules. Rocky Mountain J. Math. 23 (1993), no. 3.

  8. H. Matsumura: Commutative Ring Theory. Cambridge University Press, 1980.

  9. R. Y. Sharp: Steps in Commutative Algebra. Cambridge University Press, 1990.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints 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

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022441220553

Navigation