On superderivations and super-biderivations of trivial extensions and triangular matrix rings

Abstract

Triangular matrix rings are examples of trivial extensions. In this article, we describe the superderivations of the trivial extensions and upper triangular matrix rings, and thereby answer a question posed by Ghahramani et al. in the context of the rings above. Moreover, we show that every super-biderivation of these rings is a biderivation, and a question is posed on super-biderivations of ${\mathbb{Z}}_2-$graded rings. One of Ghahramani et al.'s results is also generalized.

Keywords:

• Super-biderivation
• superderivation
• superring
• triangular matrix ring
• trivial extension

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 16S50
• Secondary: 16W25
• 16W55