''on an algebra $ A $
algebra $ A $
3 KB (430 words) - 08:07, 6 June 2020
...that are not necessary in the given class of problems, or by a preliminary composition of a library of "standard programs" , which in its totality is sufficient
2 KB (275 words) - 17:13, 7 February 2011
...pair $(i,j)$ is the unique morphism from the object $i$ to the object $j$. Composition of morphisms is defined as follows: $(j,k)(i,j) = (i,k)$.
...).F((i,i+1)) = 0$ for any $i \in \mathbb{Z}$, cf [[Complex (in homological algebra)]]. For any [[Abelian category]] $\mathfrak{A}$ the category of sequences a
2 KB (380 words) - 11:48, 26 October 2014
algebra on the $ S $-
modules, then the composition $ \phi \circ \partial \in \mathop{\rm Der} ( R , M ) $
6 KB (945 words) - 17:32, 5 June 2020
...y finite automata form an algebra with respect to the operations of union, composition and iteration, generated by a finite set of so-called elementary events, ea
is a tribasic algebra, i.e. an algebra with three sets of elements $ A, S $
7 KB (1,008 words) - 18:48, 5 April 2020
...s to the case of affine algebraic groups. As in the analytic case, the Lie algebra of an algebraic group $ G $
...Lie algebra is defined on it by means of left-invariant derivations of the algebra of functions on $ G $ .
7 KB (1,070 words) - 21:44, 16 December 2019
is composition of morphisms, and addition is the addition of morphisms defined by the axio
algebra. Many properties of the module $ A $
4 KB (595 words) - 19:37, 5 June 2020
...rs. Double numbers have yet another appellation — paracomplex numbers. The algebra of dual numbers is considered not only over the field $ \mathbf R $
algebra and is denoted by $ I _ {A} ( M) $.
6 KB (895 words) - 19:36, 5 June 2020
...ot all subgroups) of a group, of ideals in a ring, etc. A lattice with a [[composition sequence]] is a modular lattice if and only if there exists on it a dimensi
Ore's theorem: If a modular lattice has a composition sequence and if
6 KB (942 words) - 06:28, 8 June 2024
...bra]] that is $8$-dimensional over the real numbers with a norm permitting composition that is not alternative. For more information on these algebras, their gene
...$M$ be the set of all $3 \times 3$ traceless Hermitian matrices. The Okubo algebra $P _ { 8 }$ is the [[Vector space|vector space]] over the complex numbers s
7 KB (944 words) - 10:21, 8 March 2021
is supersolvable, that is, if it has a [[Composition sequence|composition sequence]] consisting of normal subgroups with cyclic factors, then every i
then the group algebra of $ G $
10 KB (1,488 words) - 19:39, 5 June 2020
and has vertical and horizontal composition operations
...mpositions are required to be associative and unital; moreover, horizontal composition must preserve vertical units and the following interchange law is imposed:
24 KB (3,338 words) - 17:29, 7 February 2011
...) $, where $ \mathcal{E} $ is a locally free $ \mathcal{O}_{Y} $-module. A composition of projective morphisms is projective. The projectivity of a morphism is al
...ra with the $ R $-module $ A_{1} $ being of finite type and generating the algebra $ A $, and suppose that $ \operatorname{Proj}(A) $ is the set of homogeneou
3 KB (412 words) - 13:07, 17 April 2023
is a filtered associative ring with respect to the operation of composition of mappings. This ring is known as the ring of differential operators of th
is an algebra over the field of rational numbers and the module of differentials $ \Ome
5 KB (785 words) - 19:35, 5 June 2020
...endomorphisms of any algebraic system form a monoid under the operation of composition of mappings, whose unit element is the identity mapping of the underlying s
...><TR><TD valign="top">[a1]</TD> <TD valign="top"> P.M. Cohn, "Universal algebra" , Reidel (1981)</TD></TR></table>
2 KB (350 words) - 19:37, 5 June 2020
The set of $n$-tangles forms a [[monoid]]; the identity tangle and composition of tangles is illustrated in Fig.a1.
...of knots and links" J. Leech (ed.) , ''Computational Problems in Abstract Algebra'' , Pergamon Press (1969) pp. 329–358</TD></TR>
2 KB (336 words) - 09:53, 16 March 2023
The multiplication corresponds to composition of linear maps. If $A$ is the matrix of a linear map $\alpha : R^m \righta
* James E. Gentle, ''Matrix Algebra: Theory, Computations, and Applications in Statistics'', Springer Texts in
2 KB (289 words) - 19:22, 11 November 2023
Consider a [[Weil algebra|Weil algebra]] $A$ and a homomorphism $\varphi \in \operatorname{Hom}( C ^ { \infty } (
...A }$ on mappings between the $\mathbf{R} ^ { m }$ (cf. [[Weil algebra|Weil algebra]]) extends to all smooth manifolds and smooth mappings
12 KB (1,876 words) - 06:30, 15 February 2024
...no natural equivalence between the iterated tangent functor $T T$ and the composition $T ^ { * } T$ of the cotangent and the tangent functors. This implies that,
...nd all natural transformations $F \rightarrow G$ are in bijection with the algebra homomorphisms $A \rightarrow B$, see [[#References|[a1]]] for a survey. An
4 KB (674 words) - 17:02, 1 July 2020
to be the composition of a linear representation of $ G $
the Lie algebra of which is the central extension of the Lie algebra $ \mathfrak g $
5 KB (667 words) - 18:02, 13 April 2023