Principal Mappings between Posets
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-04
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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 R, it is proved that a mapping F:Idl(R)→Idl(R) is a contractive principal mapping if and only if there is a fixed ideal I∈Idl(R) such that F(J)=IJ for all J∈Idl(R).
This exploration also leads to some new problems on lattices and commutative rings.
American Psychological Association (APA)
Nai, Yuan Ting& Zhao, Dongsheng. 2014. Principal Mappings between Posets. International Journal of Mathematics and Mathematical Sciences،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-496106
Modern Language Association (MLA)
Nai, Yuan Ting& Zhao, Dongsheng. Principal Mappings between Posets. International Journal of Mathematics and Mathematical Sciences No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-496106
American Medical Association (AMA)
Nai, Yuan Ting& Zhao, Dongsheng. Principal Mappings between Posets. International Journal of Mathematics and Mathematical Sciences. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-496106
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-496106