- #1
gianeshwar
- 226
- 14
We define basis as:
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.
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.