Commutativity theorems for rings and groups with constraints on commutators
Copyright policy )Commutativity theorems for rings and groups with constraints on commutators
Let n > 1, m, t, s be any positive integers, and let R be an associative ring with identity. Suppose xt[xn, y] = [x, ym]ys for all x, y in R. If, further, R is n‐torsion free, then R is commutativite. If n‐torsion freeness of R is replaced by “m, n are relatively prime,” then R is still commutative. Moreover, example is given to show that the group theoretic analogue of this theorem is not true in general. However, it is true when t = s = 0 and m = n + 1.
torsion free rings., Commutator calculus, Rings with polynomial identity, commutative, Center, normalizer (invariant elements) (associative rings and algebras), polynomial identities, commutators, Engel conditions, QA1-939, commutativity of rings, commutative rings, n-torsion-free, Mathematics
torsion free rings., Commutator calculus, Rings with polynomial identity, commutative, Center, normalizer (invariant elements) (associative rings and algebras), polynomial identities, commutators, Engel conditions, QA1-939, commutativity of rings, commutative rings, n-torsion-free, Mathematics
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!