Cancellation property
Kürzbarkeit is a property of the elements of an algebraic structure.
- 2.1 Definition
- 2.2 Examples
Shortenable / regular items
Given a groupoid / Magma.
Definition
An element is called linkskürzbar or left regular if applies to all:
And rechtskürzbar or right- regular if for all cases:
Ie two length can be shortened or two sides regularly or just shortened or regular if c is left and rechtskürzbar.
Remark
* Is commutative, however, all three types of Kürzbarkeit are the same are generally not.
Example
- In a ring is an element if and only be shortened if it is a non- zero divisor.
Shortenable / regular semigroups
Definition
A semigroup is called shortened or regular if each one is shortened.
Examples
- The set of natural numbers with the usual addition and with the usual multiplication is a semigroup can be shortened.
- The set of natural numbers with the maximum or the minimum is not reducible semigroup.
- Algebra