-
always a
submonoid,
since the
identity elements may differ. For example, the
singleton set {0} is
closed under multiplication, and is not a
submonoid of the...
- and only if it has
finite rank. A
submonoid N of A∗ is
stable if u, v, ux, xv in N
together imply x in N. A
submonoid of A∗ is
stable if and only if it...
-
including the
empty product 1. Equivalently, a
multiplicative set is a
submonoid of the
multiplicative monoid of a ring.
Multiplicative sets are important...
-
fuzzy submonoids are
particularly interesting classes of
fuzzy subalgebras. In such a case a
fuzzy subset s of a
monoid (M,•,u) is a
fuzzy submonoid if and...
-
commutative monoid that is
finitely generated, and is
isomorphic to a
submonoid of a free
abelian group Z d , d ≥ 0 {\displaystyle \mathbb {Z} ^{d},d\geq...
-
categories are the ring
homomorphisms that map the
submonoid of the
first object into the
submonoid of the
second one. Finally, let F : D → C {\displaystyle...
- precisely, let (M, ⋅) be a monoid, and S ⊆ M. Then S* is the
smallest submonoid of M
containing S; that is, S*
contains the
neutral element of M, the...
- {Z} ,+\rangle } and does not
contain its
subalgebra (more precisely,
submonoid) ⟨ N , + ⟩ {\displaystyle \langle \mathbb {N} ,+\rangle } . However, the...
- the substructure's domain. Some
examples of
subalgebras are subgroups,
submonoids, subrings, subfields,
subalgebras of
algebras over a field, or induced...
- be a
commutative ring, and let S {\displaystyle S} be a
multiplicative submonoid of A {\displaystyle A} .
Define the
congruence relation ∼ S {\displaystyle...
