Table of Contents
Volume 2015, Article ID 183930, 6 pages
Research Article

On -Absorbing Primary Elements in Lattice Modules

Department of Mathematics, Savitribai Phule Pune University, Pune 411 007, India

Received 18 December 2014; Accepted 31 March 2015

Academic Editor: Andrei V. Kelarev

Copyright © 2015 Sachin Ballal and Vilas Kharat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let be a -lattice and let be a lattice module over . Let be a function. A proper element is said to be -absorbing primary if, for and , and together imply or , for some . We study some basic properties of -absorbing primary elements. Also, various generalizations of prime and primary elements in multiplicative lattices and lattice modules as -absorbing elements and -absorbing primary elements are unified.