...odic semi-group is separable if and only if it is a Clifford semi-group. A commutative semi-group $S$ is separable if and only if its characters separate the elem
947 bytes (144 words) - 17:58, 22 December 2023
A binary operation $*$ is commutative (or, what is the same, satisfies the law of commutativity) if in the given algebraic system the identity $a*b=b*a$ h
427 bytes (66 words) - 22:17, 26 October 2014
...as $ab=ba$. A semi-group which is reversible and obeys the [[cancellation law]] can be embedded in a [[group]], cf [[Imbedding of semi-groups]].
588 bytes (88 words) - 11:41, 2 October 2016
...ellation law [[#References|[a2]]], [[#References|[a3]]], was given for the commutative case only.
..."top">[a3]</TD> <TD valign="top"> T. Tamura, "Construction of trees and commutative Archimedean semigroups" ''Math. Nachr.'' , '''36''' : 5–6 (1968) pp.
3 KB (413 words) - 09:17, 2 April 2023
...e [[semi-group]] with unit (i.e. [[Monoid]]) satisfying the [[cancellation law]] and in which any non-invertible element $a$ is decomposable into a produc
1 KB (153 words) - 16:17, 21 December 2014
is defined (an external law of composition), such that the following axioms are satisfied:
must be commutative.
4 KB (634 words) - 07:02, 30 March 2024
from some Noetherian commutative local $ k $ -
from the category of finite-dimensional commutative $ k $ -
17 KB (2,537 words) - 22:38, 15 December 2019
...sociative binary operations $+$ and $\cdot$, satisfying the [[distributive law]]s
In most cases one also assumes that the addition is commutative and that there exists a zero element $0$ such that $a + 0 = a$ for every $a
2 KB (371 words) - 05:54, 15 April 2023
the negative index of inertia of the given form (see [[Law of inertia|Law of inertia]]; [[Quadratic form|Quadratic form]]). Sometimes the number $
be a commutative graded algebra over a commutative ring $ R $
4 KB (651 words) - 18:47, 13 January 2024
...ements $a,b,c,d$ in a distributive quasi-group are connected by the medial law: $ab\cdot cd = ac \cdot bd$, they generate a medial sub-quasi-group. In par
3 KB (425 words) - 22:16, 7 January 2017
If $R$ is a commutative ring with identity, if $R_0 = \{r\in R : r^J = r\}$, and if the matrix of $
Let $R$ be commutative. Then a Hermitian form $\phi$ on $X$ gives rise to a quadratic form $Q(x)=\
5 KB (831 words) - 17:13, 9 October 2016
with an additional commutative and associative binary operation, called multiplication (and denoted by $
...e majority of concepts and results have an analogue (or an application) in commutative rings (see [[#References|[1]]]).
8 KB (1,218 words) - 08:02, 6 June 2020
...ciative]] and [[Commutativity|commutative]] and satisfy the [[distributive law]]; 1 is the [[neutral element]] for multiplication, i.e. $a \times 1 = a =
2 KB (319 words) - 19:08, 5 February 2016
...satisfying the law $x^n=1$ is locally finite, then any semi-group with the law $x^{n+1}=x$ is locally finite [[#References|[6]]]. A semi-group that has a
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.../c025970/c02597024.png" /> change according to the so-called contravariant
law
....encyclopediaofmath.org/legacyimages/c/c025/c025970/c02597044.png" /> be a
commutative ring with unit element and <img align="absmiddle" border="0" src="https://w
10 KB (1,407 words) - 17:29, 7 February 2011
corresponds the conservation law
then by Stokes' theorem the integral of the conservation law $ v $
16 KB (2,336 words) - 08:02, 6 June 2020
of such a loop are connected by the associative law, that is, if
...automorphism of an IP-loop induces an automorphism in its kernel, and in a commutative Moufang loop any pseudo-automorphism is an automorphism.
8 KB (1,291 words) - 06:59, 30 March 2024
A set with one binary operation satisfying the law of [[associativity]]. A semi-group is a generalization of the concept of a
...with a [[cancellation law]] and [[regular semi-group]]s). The cancellation law and regularity are examples of restrictions which in a sense constitute wea
17 KB (2,435 words) - 09:18, 2 April 2023
...hich is the quantum analogue of the probabilistic notion of convergence in law (cf. [[Convergence in probability|Convergence in probability]]; [[Quantum p
...I.V. Volovich, "The master field for half-planar diagrams and free non-commutative random variables" ''Modern Physics Letters'' (1996)</TD></TR><TR><TD vali
8 KB (1,210 words) - 08:23, 6 June 2020
There is an analogue of Pontryagin duality for non-commutative groups (the duality theorem of Tannaka–Krein) (see , [[#References|[6]]],
...>[1]</TD> <TD valign="top"> L.S. Pontryagin, "The theory of topological commutative groups" ''Ann. of Math.'' , '''35''' : 2 (1934) pp. 361–388</TD></TR>
10 KB (1,483 words) - 17:06, 13 June 2020