A study on (m, n)-centralizer finite rings.

For any m distinct elements r1, r2, · · ·, rm in a ring R, the m-element centralizer of {r1, r2, · · ·, rm} in R is defined as CR({r1, r2, · · ·, rm}) = {s ∈ R | sr1 = r1s, sr2 = r2s, . . ., srm = rms}, where m ∈ N with m ≽ 2. We define the set of all distinct m-element centralizers in a ring R by m - Cent(R), where m ∈ N with m ≽ 2. Further, R is called (m, n)-centralizer ring if |m - Cent(R)| = n, where n ∈ N. In this paper, we characterize some of the (m, n)-centralizer finite rings for n ≼ 7. [ABSTRACT FROM AUTHOR]