Jordan isomorphisms of finitary incidence algebras

Abstract

Let X be a partially ordered set, R a commutative 2-torsionfree unital ring and FI(X, R) the finitary incidence algebra of X over R. In this note we prove that each R-linear Jordan isomorphism of FI(X, R) onto an R-algebra A is the near-sum of a homomorphism and an anti-homomorphism.

Keywords:

• Jordan isomorphism
• near-sum
• homomorphism
• anti-homomorphism
• finitary incidence algebra

AMS Subject Classifications:

• Primary: 16S50
• 17C50
• Secondary: 16W10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first and second authors were partially supported by Fundação Araucária [Convênio 212/14]. The third author thanks the Department of Mathematics of Maringá State University for its warm hospitality and financial support.