- #1
dijkarte
- 191
- 0
When we talk about an abstract binary operation *:SxS --> S
We say that an identity element "e" exists when e * x = x * e = x, (x; e belong to S)
Now my questions:
1) If the operation is not commutative, does not this imply no identity? since e * x != x * e necessarily?
2) Does e * x = x imply x * e = x? And if one side is true, can we still say that * has an identity restricted to one side?
3) Is there cases where not all x's of the set S have the same identity wrt operation *?
These questions are regardless of any kind of algebraic structure.
Thanks.
We say that an identity element "e" exists when e * x = x * e = x, (x; e belong to S)
Now my questions:
1) If the operation is not commutative, does not this imply no identity? since e * x != x * e necessarily?
2) Does e * x = x imply x * e = x? And if one side is true, can we still say that * has an identity restricted to one side?
3) Is there cases where not all x's of the set S have the same identity wrt operation *?
These questions are regardless of any kind of algebraic structure.
Thanks.