(⊙,∨)-Derivations on MV-algebras

作者：Zhao, Xueting; Gan, Aiping; Yang, Yichuan^*

来源：Soft Computing, 2024, 28(3): 1833-1849.

DOI：10.1007/s00500-023-09384-2

• MV-algebra
• Derivation
• Direct product
• Complete lattice
• Boolean center
• Ideal
• Fixed point set

Let A be an MV-algebra. An (circle dot,boolean OR)-derivation on A is a map d : A -> A satisfying: d(x circle dot y) = (d(x) circle dot y) boolean OR (x circle dot d(y)) for all x, y is an element of A. This paper initiates the study of (circle dot,boolean OR)-derivations on MV-algebras. Several families of (circle dot,boolean OR)-derivations on an MV-algebra are explicitly constructed to give realizations of the underlying lattice of an MV-algebra as lattices of (circle dot,boolean OR)-derivations. Furthermore, (circle dot,boolean OR)-derivations on a finite MV-chain are enumerated and the underlying lattice is described.

• 单位
  北京航空航天大学; 江西师范大学