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In this paper, we consider a conjecture of I. N. Herstein for local commutators of symmetric elements and unitary elements of division rings. For example, we show that if $D$ is a finite dimensional division ring with involution $\star$ and if $a\in D^*=D\backslash\{0\}$ such that local commutators $axa^{-1}x^{-1}$ at $a$ are radical over the center $F$ of $D$ for every $x\in D^*$ with $x^\star=x$, then either $a\in F$ or $\dim_{F}D= 4$.
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참고문헌 (22)
참고문헌 신청
K. I. Beidar / 1996 / Rings with Generalized Identi-ties / Marcel Dekker, Inc.
Mai Hoang Bien / 2015 / ON SOME SUBGROUPS OF D∗ WHICH SATISFY A GENERALIZED GROUP IDENTITY / 대한수학회보 52(4):1353~1363
M. H. Bien / 2016 / Subnormal subgroups in division rings with generalized power central group identities / Arch. Math. (Basel) 106(4):315~321
M. Chacron / 1975 / Powers of skew and symmetric elements in division rings / Houston J. Math 1(1):15~27
K. Chiba / 1994 / Skew elds with a nontrivial generalised power central rational identity / Bull. Austral. Math. Soc 49(1):85~90
Mai Hoang Bien / 2015 / ON SOME SUBGROUPS OF D∗ WHICH SATISFY A GENERALIZED GROUP IDENTITY / 대한수학회보 52(4):1353~1363
M. H. Bien / 2016 / Subnormal subgroups in division rings with generalized power central group identities / Arch. Math. (Basel) 106(4):315~321
M. Chacron / 1975 / Powers of skew and symmetric elements in division rings / Houston J. Math 1(1):15~27
K. Chiba / 1994 / Skew elds with a nontrivial generalised power central rational identity / Bull. Austral. Math. Soc 49(1):85~90
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