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On derivations of commutative multiplicative semilattices.

Authors :
Wang, Jun Tao
Borumand Saeid, Arsham
Wang, Mei
Source :
Journal of Intelligent & Fuzzy Systems; 2018, Vol. 35 Issue 1, p957-966, 10p
Publication Year :
2018

Abstract

In this paper, we investigate related properties of some particular derivations and give some characterizations of regular derivations in commutative multiplicative semilattices. Also we give some characterizations of zero derivations in prime commutative multiplicative semilattices. Then we prove that the set of all prefect derivations ideals on commutative multiplicative semilattices with prefect derivations can form a complete Heyting algebra and obtain that there exists a one to one correspondence between the set of all prefect derivations ideals on commutative multiplicative semilattices with prefect derivations and its quotient structure. Finally, we show that the structure of an idempotent commutative quantale is completely determined by its set of all principal derivations. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10641246
Volume :
35
Issue :
1
Database :
Complementary Index
Journal :
Journal of Intelligent & Fuzzy Systems
Publication Type :
Academic Journal
Accession number :
131004810
Full Text :
https://doi.org/10.3233/JIFS-171838