A semigroup is said to be right subcommutative if for any two of its elements and , there exists its element such that
If is both left subcommutative and right subcommutative, it is subcommutative.
The commutativity is a special case of all the three kinds of subcommutativity.
Example 1. The following operation table defines a right subcommutative semigroup which is not left subcommutative (e.g. ):
Remark. One uses the above also for a ring if its multiplicative semigroup satisfies the corresponding requirements.
- 1 S. Lajos: “On -ideals in subcommutative semigroups”. – Elemente der Mathematik 24 (1969).
- 2 V. P. Elizarov: “Subcommutative Q-rings”. – Mathematical notes 2 (1967).
|Date of creation||2013-03-22 19:13:45|
|Last modified on||2013-03-22 19:13:45|
|Last modified by||pahio (2872)|