Affiliations: [a] School of Science, Xi’an Shiyou University, Xi’an, Shaanxi, China
| [b] Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran
| [c] Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
| [d]
Xi’an Traffic Engineering Institute, Xi’an, China
Correspondence:
[*]
Corresponding author. Jun Tao Wang, School of Science, Xi’an Shiyou University, Xi’an 710065, Shaanxi, China. E-mail: [email protected].
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.
Keywords: Multiplicative semilattice, prefect derivation, fixed point set, quantale
