Question

In: Advanced Math

a. Give an example of a finitely generated module over an integral domain which is not...

a. Give an example of a finitely generated module over an integral domain which is not isomorphic to a direct sum of cyclic modules.

b. Let R be an integral domain and let M=<m_1,...,m_r> be a finitely generated module. Prove that rank of M is less than or equal to r.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
Next > < Previous

Related Solutions

Prove that every finite integral domain is a field. Give an example of an integral domain...
Prove that every finite integral domain is a field. Give an example of an integral domain which is not a field. Please show all steps of the proof. Thank you!!
A finitely generated module is projective if and only if it is a direct summand of...
A finitely generated module is projective if and only if it is a direct summand of a finitely generated free module. I am having trouble grasping the "finitely generated" part.
Find an example with an explanation of Integral domain but not domain with factorization Domain with...
Find an example with an explanation of Integral domain but not domain with factorization Domain with factorization but not unique factorization domains Domain with factorization but not Noetherian domains    Unique factorization domains but not Noetherian unique factorization domains Noetherian Domains but not Noetherian Unique factorization domains Noetherian Unique factorization domains but not principal ideal domain principal ideal domain but not Euclidean domains Euclidean domain but not field
For example, a definite integral of a velocity function gives the accumulated distance over the period....
For example, a definite integral of a velocity function gives the accumulated distance over the period. You should also be growing more comfortable with how the units work – for example, integrating meters per second with respect to seconds gives meters.Your job is to find an article that refers to a definite integral. It is possible that you will be able to find an explicit mention of a definite integral. Much more likely, though, the definite integral will be implied...
1.2.2*. Find an example to show that the phrase "finitely many" is necessary in the statement...
1.2.2*. Find an example to show that the phrase "finitely many" is necessary in the statement of Lemma 1.2.3 (iii). Lemma 1.2.3. (i) Rn and empty set are open in Rn (ii) The union ofo pen subset of Rn is open. (iii) The intersect of finitely many open subsets Rn is open.
Describe the method of establishing and evaluating for a triple integral: Give an example using one...
Describe the method of establishing and evaluating for a triple integral: Give an example using one of the following options: a) iterated triple integral b) use of spherical coordinates c) use of cylinder coordinates
2 examples of each 1-Direct Products and Finitely Generated Abelian Groups Direct Product 2-Homomorphisms
2 examples of each 1-Direct Products and Finitely Generated Abelian Groups Direct Product 2-Homomorphisms
Let (Z, N, +, ·) be an ordered integral domain. Let {x1, x2, . . ....
Let (Z, N, +, ·) be an ordered integral domain. Let {x1, x2, . . . , xn} be a subset of Z. Prove there exists an i, 1 ≤ i ≤ n such that xi ≥ xj for all 1 ≤ j ≤ n. Prove that Z is an infinite set. (Remark: How do you tell if a set is infinite??)
(8) show that if R is an integral domain with unit element, then any unit in...
(8) show that if R is an integral domain with unit element, then any unit in R[x] is also a unit in R.
let D be an integral domain. prove that an element of D[x] is a unit if...
let D be an integral domain. prove that an element of D[x] is a unit if an only if it is a unit in D.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT