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Results tagged with semigroups-and-monoids
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user 5963
A semigroup is a set $S$ together with a binary operation that is associative. Examples of semigroups are the set of finite strings over a fixed alphabet (under concatenation) and the positive integers (under addition, maximum, or minimum). A monoid is a semigroup with a neutral element. Of course, any group is also a monoid/semigroup.
9
votes
Accepted
Semiring naturally associated to any monoid?
It is at least sometimes called a "monoid semiring" by analogy with "group ring". As such it would be notated $S = \mathbb{N_0}[M]$ (or $\mathbb{N}[M]$ depending how you define things).
By the way, …
- 8,501
7
votes
on the set of numbers generated by integer linear combination of two real numbers.
Yes, the set $X = a\mathbb{N} + b\mathbb{N}$ is order-isomorphic to $\mathbb{N}$.
For any positive real $k$ the set $X\cap [0,k]$ is finite. Indeed, to have $ap+bq \leq k$ for $p,q\in\mathbb{N}$ we …
- 8,501