A Note on Principal 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 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 $r$,...
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The paper gives a reenement to a well known and easy-to-prove result of basic ideal theory: If an ideal I is contained in the union of a given nite collection of ideals, with at most two of them not prime, I must be contained in one of them. The proposition, stated in this way, leaves out the special structure of the ring under consideration. We show that the lower bound implicit in the proposi...
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ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 1957
ISSN: 0018-2079
DOI: 10.32917/hmj/1555639497