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Results tagged with semigroups-and-monoids
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user 40520
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.
1
vote
0
answers
103
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Lower periodic subsets of groups and semigroups
Suppose that $A$ and $B$ are subsets of a group or semigroup. We call $A$ left
upper [resp. lower] $B$-periodic if $BA\subseteq A$
[resp. $A\subseteq BA$]. If $A$ is both left upper and
lower $B$-pe …
- 995
4
votes
1
answer
189
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Some questions about homogroups
Every semigroup containing an ideal subgroup is called a homogroup. Let $(S,\cdot)$ be homomgroup, hence it contains an ideal $I$ that is also a subgroup. It is easy to see that $I$ is the least ideal …
- 995
3
votes
0
answers
79
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Semigroups containing an ideal with a local identity
I'm looking for some classes of semigroups containing a (proper) ideal with a local identity (i.e., ideal submonoid). Can somebody give some examples or/and theorems for the followings cases:
(a) No …
- 995
4
votes
1
answer
432
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Regarding a new algebraic structure
By "left semigroup-joined-semigroup" I mean an algebraic structures $(S,\cdot,*)$ such that both $\cdot,*$ are associative, and the following property holds (see this )
$$
x*(y\cdot z)=x*y*z\;\; ; \ …
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