Some conditions for finiteness and commutativity of rings
نویسندگان
چکیده
منابع مشابه
A commutativity-or-finiteness condition for rings
In view of this result, it was conjectured that any ring with only finitely many noncentral subrings is either finite or commutative. It is our principal goal to prove this conjecture; and in the process we provide a new proof of Theorem 1.1. For any ring R, the symbols N, D, Z , and ℘(R) will denote, respectively, the set of nilpotent elements, the set of zero divisors, the center, and the pri...
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Let $R$ be a $*$-prime ring with center $Z(R)$, $d$ a non-zero $(sigma,tau)$-derivation of $R$ with associated automorphisms $sigma$ and $tau$ of $R$, such that $sigma$, $tau$ and $d$ commute with $'*'$. Suppose that $U$ is an ideal of $R$ such that $U^*=U$, and $C_{sigma,tau}={cin R~|~csigma(x)=tau(x)c~mbox{for~all}~xin R}.$ In the present paper, it is shown that if charac...
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let $r$ be a $*$-prime ring with center $z(r)$, $d$ a non-zero $(sigma,tau)$-derivation of $r$ with associated automorphisms $sigma$ and $tau$ of $r$, such that $sigma$, $tau$ and $d$ commute with $'*'$. suppose that $u$ is an ideal of $r$ such that $u^*=u$, and $c_{sigma,tau}={cin r~|~csigma(x)=tau(x)c~mbox{for~all}~xin r}.$ in the present paper, it is shown that...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1990
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171290000771