Functional identities of degree 2 in triangular rings revisited

Abstract

Using the notion of the maximal left ring of quotients, our recent result on the solutions of functional identity in triangular rings is generalized. Consequently, generalizations of known results on commuting additive maps and generalized inner biderivations of triangular rings are obtained.

Keywords:

• functional identity
• commuting map
• biderivation
• triangular ring
• upper triangular matrix ring
• nest algebra
• maximal left ring of quotients
• extended centroid

AMS Subject Classifications:

• 16R60
• 16S50
• 47L35