Prime Rings with Maximal Annihilator and Maximal Complement Right Ideals
نویسندگان
چکیده
منابع مشابه
A note on maximal non-prime ideals
The rings considered in this article are commutative with identity $1neq 0$. By a proper ideal of a ring $R$, we mean an ideal $I$ of $R$ such that $Ineq R$. We say that a proper ideal $I$ of a ring $R$ is a maximal non-prime ideal if $I$ is not a prime ideal of $R$ but any proper ideal $A$ of $R$ with $ Isubseteq A$ and $Ineq A$ is a prime ideal. That is, among all the proper ideals of $R$,...
متن کاملRings with no Maximal Ideals
In this note we give examples of a ring that has no maximal ideals. Recall that, by a Zorn’s lemma argument, a ring with identity has a maximal ideal. Therefore, we need to produce examples of rings without identity. To help motivate our examples, let S be a ring without identity. We may embed S in a ring R with identity so that S is an ideal of R. Notably, set R = Z⊕S, as groups, and where mul...
متن کاملa note on maximal non-prime ideals
the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$, we mean an ideal $i$ of $r$ such that $ineq r$. we say that a proper ideal $i$ of a ring $r$ is a maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...
متن کاملMAXIMAL DIVISORIAL IDEALS AND t-MAXIMAL IDEALS
We give conditions for a maximal divisorial ideal to be t-maximal and show with examples that, even in a completely integrally closed domain, maximal divisorial ideals need not be t-maximal.
متن کاملFuzzy Maximal Ideals of Gamma Near-Rings∗
Fuzzy maximal ideals and complete normal fuzzy ideals in Γ-near-rings are considered, and related properties are investigated.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1965
ISSN: 0002-9939
DOI: 10.2307/2035619