Aiping Gan

activity

20212024

collaborators

5 papers

math.RA2024

Difference operators on lattices

Aiping Gan, Li Guo

A differential operator of weight $λ$ is the algebraic abstraction of the difference quotient $d_{λ} (f) (x) := (f (x + λ) - f (x)) / λ$ , including both the derivation as $λ$ approaches…

math.RA2023

Ideal-based zero-divisor graph of MV-algebras

Aiping Gan, Huadong Su, Yichuan Yang

Let $(A, \oplus, *, 0)$ be an MV-algebra, $(A, ⊙, 0)$ be the associated commutative semigroup, and $I$ be an ideal of $A$ . Define the ideal-based zero-divisor graph $Γ_{I} (A)$ …

math.RA2023

( $⊙$ , $\lor$ )-derivations on MV-algebras

Xueting Zhao, Aiping Gan, Yichuan Yang

Let $A$ be an MV-algebra. An $(⊙, \lor)$ -derivation on $A$ is a map $d : A \to A$ satisfying: $d (x ⊙ y) = (d (x) ⊙ y) \lor (x ⊙ d (y))$ for all $x, y \in A$ . This paper i…

math.RA2021

Integral operators on lattices

Aiping Gan, Li Guo

As an abstraction and generalization of the integral operator in analysis, integral operators (known as Rota-Baxter operators of weight zero) on associative algebras and Lie algebr…

math.RA2021

On differential lattices

Aiping Gan, Li Guo

This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d : L \to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomor…

Difference operators on lattices

Ideal-based zero-divisor graph of MV-algebras

(⊙, ∨)-derivations on MV-algebras

Integral operators on lattices

On differential lattices

( $⊙$ , $\lor$ )-derivations on MV-algebras