A note on powers of 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 کاملComparing Powers and Symbolic Powers of Ideals
We develop tools to study the problem of containment of symbolic powers I(m) in powers I for a homogeneous ideal I in a polynomial ring k[P ] in N + 1 variables over an arbitrary algebraically closed field k. We obtain results on the structure of the set of pairs (r, m) such that I(m) ⊆ I. As corollaries, we show that I2 contains I(3) whenever S is a finite generic set of points in P2 (thereby ...
متن کاملA Note on Unions of Ideals and Cosets of Ideals
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...
متن کاملA Note on Sums of Powers
We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.
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 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: Journal of Pure and Applied Algebra
سال: 1998
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(96)00111-9