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International Journal of Mathematics and Mathematical Sciences - Volume 2014 2014, Article ID 754019, 9 pages -

Research ArticleMathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616

Received 14 January 2014; Accepted 7 April 2014; Published 4 May 2014

Academic Editor: Michael M. Tom

Copyright © 2014 Yuan Ting Nai and Dongsheng Zhao. 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.


We introduce and study principal mappings between posets which generalize the notion of principal elements in a multiplicative lattice, in particular, the principal ideals of a commutative ring. We also consider some weaker forms of principal mappings such as meet principal, join principal, weak meet principal, and weak join principal mappings which also generalize the corresponding notions on elements in a multiplicative lattice, considered by Dilworth, Anderson and Johnson. The principal mappings between the lattices of powersets and chains are characterized. Finally, for any PID , it is proved that a mapping is a contractive principal mapping if and only if there is a fixed ideal such that for all . This exploration also leads to some new problems on lattices and commutative rings.

Author: Yuan Ting Nai and Dongsheng Zhao



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