We define basis as:(adsbygoogle = window.adsbygoogle || []).push({});

Let M be a module over a ring R with unity and let S be a subset of M. Then S is called a basis of M if

1. M is generated by S 2. S is linearly independent set.

Also we define free module as

An R module M is called a free module if there exists a subset S of M s.t.S generates M and S is linearly independent set.

NOW my QUESTIONS are :

1.Does a free module require unity?

2.Can a free module be basis?

3.Please tell me also the difference between the notations {0},{},(0) in reference to modules.

* I am still a learner in this area of mathematics.

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# Basis of module and Free module

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