The Endomorphism Ring of an Artinian Module whose Homogeneous Length is Finite
نویسندگان
چکیده
منابع مشابه
An Endomorphism Whose Square Is Bernoulli
One of the corollaries of Ornstein’s isomorphism theorem is that if (Y, S, ν) is an invertible measure preserving transformation and (Y, S, ν) is isomorphic to a Bernoulli shift then (Y, S, ν) is isomorphic to a Bernoulli shift. In this paper we show that noninvertible transformations do not share this property. We do this by exhibiting a uniformly 2-1 endomorphism (X, σ, μ) which is not isomor...
متن کاملIRRELEVANT ATTACHED PRIME IDEALS OF A CERTAIN ARTINIAN MODULE OVER A COMMUTATIVE RING
Let M be an Artinian module over the commutative ring A (with nonzero identity) and a p spec A be such that a is a finitely generated ideal of A and aM = M. Also suppose that H = H where H. = M/ (0: a )for i
متن کاملComputing the endomorphism ring of an ordinary elliptic curve over a finite field
We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field Fq . Under suitable heuristic assumptions, both have subexponential complexity. We bound the complexity of the first algorithm in terms of log q , while our bound for the second algorithm depends primarily on log |DE |, where DE is the discriminant of the order isomorphic to En...
متن کاملThe length of Artinian modules with countable Noetherian dimension
It is shown that if $M$ is an Artinian module over a ring $R$, then $M$ has Noetherian dimension $alpha $, where $alpha $ is a countable ordinal number, if and only if $omega ^{alpha }+2leq it{l}(M)leq omega ^{alpha +1}$, where $ it{l}(M)$ is the length of $M$, $i.e.,$ the least ordinal number such that the interval $[0, it{l}(M))$ cannot be embedded in the lattice of all su...
متن کاملThe centralizer of an element in an endomorphism ring
We prove that the centralizer Cφ ⊆ HomR(M,M) of a nilpotent endomorphism φ of a finitely generated semisimple left R-module RM (over an arbitrary ring R) is the homomorphic image of the opposite of a certain Z(R)-subalgebra of the full m×m matrix algebra Mm×m(R[t]), where m is the dimension (composition length) of ker(φ). If R is a finite dimensional division ring over its central subfield Z(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: Proceedings of the American Mathematical Society
سال: 1982
ISSN: 0002-9939
DOI: 10.2307/2043381