Generalisation of n-centraliser rings and their graphs - Chan, Tai Chong (2024)
Let Cent(R) denote the set of all distinct centralisers in a ring R. A ring R is said to be an n-centraliser ring if |Cent(R)| = n, where n 2 N. The question of how the number of distinct centralisers in a ring can influence its structure and commutativity has recently captured the attention of several researchers. Therefore, the study of the n-centraliser rings is a prospective research topic in ring theory. In this dissertation, we first investigate the characterisation for all n-centraliser finite rings for n 2 {6, 7, 8, 9, 10, 11} and compute their commuting probabilities. Subsequently, we classify the structures for all finite rings in which the cardinality of the maximal non-commuting set is 5.