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.

Expert Solution

P is R module then P is projective iff P is isomorphic to direct summand of free R module.

Colby Messinger answered 2 years ago

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.

2 examples of each 1-Direct Products and Finitely Generated Abelian Groups Direct Product 2-Homomorphisms

Analyse TAT as a projective technique.

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If R is a P.I.D. then an R-module Q is injective if and only if rQ=Q...

If R is a P.I.D. then an R-module Q is injective if and only if rQ=Q for every nonzero r in R.

Government imposes direct taxes on the income earned and generated by businesses. Are these taxes burden...

Government imposes direct taxes on the income earned and generated by businesses. Are these taxes burden on the public or these taxes are an instrument of social and economic policy in the hands on government. Express your opinion with suitable examples.

Determine whether there is an integer n > 1 such that there is a projective plane...

Determine whether there is an integer n > 1 such that there is a projective plane of order n (i.e. with n + 1 points on each line) such that n ̸= pk for any prime number p and integer k ≥ 1.

what are projective techniques and how can they be used profitably

Both Module 4 and Chapter 6 discuss the importance of two elements of a direct approach...

Both Module 4 and Chapter 6 discuss the importance of two elements of a direct approach message: a specific subject line that summarizes the message a clear message purpose or main point in the first sentence(s) This week, when you write emails, practice writing subject lines and message openings that follow the guidelines in the textbook and the Module. Then, post the subject line and first few lines of an email you wrote -- either a request, or a reply...

Consider the Prisoners’ Dilemma that is played for two rounds. Is there a NE of finitely-repeated...

Consider the Prisoners’ Dilemma that is played for two rounds. Is there a NE of finitely-repeated Prisoner’s Dilemma which is different from the SPE? Is there a NE outcome which is different from the SPE outcome?

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.

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