Binary operations-equivalence classes

Reference no: EM13132566

Let M be a commutative monoid. Define a relation ~ on M by a ~ b if a = bu for some unit u.

(a) Show that ~ is an equivalence on M and if a* deontes the equivalence class of a, let M* = {a*| a belongs to M} denote the set of all equivalence classes. Show that a*b* = (ab)* is a well-defined operation on M* deontes.

(b) If M* is as in (a), show that M* is a commutative monoid in which the identity 1* is the only unit.

Reference no: EM13132566

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