1. Since the identity element of a monoid is unique, one can alternately define the identity function on M to be this identity element.

2. The identity element of arbitrary cyclic code over GF(2) can be found out by use of this method.

3. In other words, F respects addition, multiplication and identity element.

4. The author discusses the problem of the semidirect products of completely simple semigroups without identity element.

5. Each subgroup contains exactly one idempotent , namely the identity element of the subgroup.

6. The author discusses the problem of the semidirect products of completely simple semigroups identity element.

7. If we consider the integers with ordinary multiplication we have closure, associativity, and identity element.

8. In this paper the concepts of strongly closed set of hyperlattices and scalar-upper bound identity element are introduced.