Q4) Draw the lattice of the Z-modulethis module.and then determine direct summand of30ZQ5) Show that:(1) Any subset of Qz has more than one element is not free.(2)Qz has no minimal and no maximal submodules.(3) Let a A B and B BBoa is an epimorphismC be homomorphisms. Then, we haveẞ is an epimorphism.

import matplotlib.pyplot as plt import networkx as nx # Create a directed graph for the lattice…

Answered: Q4) Draw the lattice of the Z-module…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 7E: Write 20 as the direct sum of two of its nontrivial subgroups.

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