A commutativity theorem for power-associative rings

Autor:	Adil Yaqub, D. L. Outcalt
Rok vydání:	1970
Předmět:	Combinatorics Discrete mathematics Ring (mathematics) Identity (mathematics) Finite field Integer General Mathematics Ideal (ring theory) Commutative property Associative property Mathematics Power (physics)
Zdroj:	Bulletin of the Australian Mathematical Society. 3:75-79
ISSN:	1755-1633 0004-9727
DOI:	10.1017/s0004972700045676
Popis:	Let R be a power-associative ring with identity and let I be an ideal of R such that R/I is a finite field and x ≡ y (mod I) implies x2 = y2 or both x and y commute with all elements of I. It is proven that R must then be commutative. Examples are given to show that R need not be commutative if various parts of the hypothesis are dropped or if “x2 = y2” is replaced by “xk = yk” for any integer k > 2.
Databáze:	OpenAIRE
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