Principal Mappings between Posets

Joint Authors

Zhao, Dongsheng
Nai, Yuan Ting

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

Mathematics

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