Beginning and Intermediate Algebra
6th Edition
ISBN: 9781260673531
Author: Miller, Julie, O'Neill, Molly, Hyde, Nancy
Publisher: McGraw-Hill Education
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Question
Chapter 15.7, Problem 72PE
To determine
To calculate: The number of ways in which it can occur that all the 5 drawn cards are of heart if a standard deck of 52 cards it has four suits (clubs, diamonds, hearts, and spades). Each suit has 13 cards. The hearts and diamonds are red cards, and the clubs and spades are black cards.
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Q.1) Classify the following statements as a true or false statements:
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a. A simple ring R is simple as a right R-module.
b. Every ideal of ZZ is small ideal.
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c. A nontrivial direct summand of a module cannot be large or small submodule.
d. The sum of a finite family of small submodules of a module M is small in M.
e. The direct product of a finite family of projective modules is projective
f. The sum of a finite family of large submodules of a module M is large in M.
g. Zz contains no minimal submodules.
h. Qz has no minimal and no maximal submodules.
i. Every divisible Z-module is injective.
j. Every projective module is a free module.
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Q.4) Give an example and explain your claim in each case:
a) A module M which has a largest proper submodule, is directly indecomposable.
b) A free subset of a module.
c) A finite free module.
d) A module contains no a direct summand.
e) A short split exact sequence of modules.
Chapter 15 Solutions
Beginning and Intermediate Algebra
Ch. 15.1 - Prob. 1SPCh. 15.1 - Prob. 2SPCh. 15.1 - Prob. 3SPCh. 15.1 - Prob. 4SPCh. 15.1 - Prob. 5SPCh. 15.1 - Prob. 6SPCh. 15.1 - Prob. 7SPCh. 15.1 - Prob. 8SPCh. 15.1 - Prob. 9SPCh. 15.1 - Prob. 1PE
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