A classification of regressive transformation semigroups on chains

作者：Udomkavanich Patanee^*; Jitjankarn Phichet

来源：Semigroup Forum, 2012, 85(3): 559-570.

DOI：10.1007/s00233-012-9438-7

• Isomorphism theorems
• Regressive transformation semigroups
• Chains

For each subchain X%26apos; of a chain X, let T (RE) (X,X%26apos;) denote the semigroup under composition of all full regressive transformations, alpha:X -%26gt; X%26apos; satisfying x alpha a parts per thousand currency signx for all xaX. Necessary and sufficient conditions for T (RE) (X,X%26apos;) and T (RE) (Y,Y%26apos;) to be isomorphic are given. This isomorphism theorem is applied to classify the semigroup of regressive transformations T (RE) (X,X%26apos;) where X is one of several familiar subchains of a%26quot;e, the chain of real numbers.

• 出版日期2012-12