Reconstructability of a monounary algebra from its second centralizer

ABSTRACT

The paper deals with monounary algebras and their first and second centralizers. First we show that operations are equivalent with respect to the first centralizer if and only if they are equivalent with respect to the second centralizer. We find necessary and sufficient conditions for an operation when the operation is uniquely determined by its centralizer. In this case, a sequence of steps for a description of the operation is presented.

KEYWORDS:

• Endomorphism
• first centralizer
• monounary algebra
• second centralizer

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 08A60
• 08A35
• 20M20