If you need an accessible version of this item please contact JSTOR User Support

Principal Elements of Lattices of Ideals

P. J. McCarthy
Proceedings of the American Mathematical Society
Vol. 30, No. 1 (Sep., 1971), pp. 43-45
DOI: 10.2307/2038216
Stable URL: http://www.jstor.org/stable/2038216
Page Count: 3
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Principal Elements of Lattices of Ideals
Preview not available

Abstract

The notion of principal element of a commutative multiplicative lattice was introduced by Dilworth. In this note the principal elements of the lattice of ideals of a commutative ring with unity $R$ are characterized as those ideals of $R$ which are finitely generated and locally principal ideals. It follows that a regular ideal of $R$ is a principal element of the lattice of ideals of $R$ if and only if it is invertible.

Page Thumbnails

  • Thumbnail: Page 
43
    43
  • Thumbnail: Page 
44
    44
  • Thumbnail: Page 
45
    45