Latifa Bedda, Abdelkarim Boua, "Some Results on Partially Ordered Sets Involving Permuting n-derivations," WSEAS Transactions on Mathematics, vol. 23, pp. 553-560, 2024, DOI:10.37394/23206.2024.23.58
Latifa Bedda, Abdelkarim Boua. Some Results on Partially Ordered Sets Involving Permuting n-derivations.
WSEAS Transactions on Mathematics. 2024;23:553-560. 10.37394/23206.2024.23.58
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Some Results on Partially Ordered Sets Involving Permuting n-derivations
Authors: ,
Abstract: The main objective of the present work, as a generalization of derivation, is to give the concept of <i>permuting
n-derivations on partially ordered sets (posets)</i>. Several associated theorems and fondamental properties
involving permuting n-derivations are presented. Moreover, we demonstrate that if $$D$$ is a permuting n-derivation
on poset $$G$$ with the greatest element 1 and the trace $$δ$$, then $$δ(1) = 1$$ if and only if $$δ$$ is an identity on $$G$$. Furthermore,
we discuss the relations among derivations, ideals and fixed sets in posets.
Keywords:
Partially ordered sets (posets), Upper bound, Lower bound, Directed poset, Derivation, Permuting
n-derivations, Lower homomorphism, Fixed set
Pages: 553-560 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 23, 2024, Art. #58 DOI: 10.37394/23206.2024.23.58
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