$#A+1 = 13 n = 0
A set $ M $
2 KB (242 words) - 16:40, 31 March 2020
$#A+1 = 49 n = 0
x ^ {n} \equiv a ( \mathop{\rm mod} m ) ,
5 KB (717 words) - 08:27, 6 June 2020
or their subgroups, given certain special extensions of the ground ring $ R $(
...(cf. [[Regular ring (in commutative algebra)|Regular ring (in commutative algebra)]]) and let $ R[t _{1} \dots t _{n} ] $
7 KB (972 words) - 19:10, 5 April 2023
Two subextensions $A$ and $B$ of an extension $\def\O{\Omega}\O$ of $k$ are called linearly disj
subalgebra generated by $A$ and $B$ in $\O$ is (isomorphic to) the
1 KB (259 words) - 22:07, 5 March 2012
$#A+1 = 129 n = 0
$#C+1 = 129 : ~/encyclopedia/old_files/data/W098/W.0908080 Witt ring
9 KB (1,359 words) - 08:29, 6 June 2020
...hat discrete versions of the [[Bellman equation]] can be treated as linear over idempotent semi-rings. The so-called (finite-dimensional) generalized stati
...interesting numerical algorithm, then there is a good chance that its semi-ring analogues are important and interesting as well" , [[#References|[a9]]], [[
7 KB (1,079 words) - 20:39, 16 November 2023
$#A+1 = 68 n = 0
A submodule $ A $
4 KB (701 words) - 08:04, 21 January 2024
''on a product of modules $V\times W$''
A
6 KB (1,157 words) - 08:58, 9 December 2016
$#A+1 = 235 n = 0
''logarithmic norm, norm on a field''
14 KB (2,135 words) - 08:27, 6 June 2020
on a left $R$-module $X$'' is
a mapping $\def\phi{\varphi}\phi:X\times X \to R$ that is linear in the first
5 KB (831 words) - 17:13, 9 October 2016
where $x,y,\dots,w$ are variables and $A,B,\dots,D$ (the ''coefficients'' of the polynomial) and $k,l,\dots,t$ (the
...zero powers. When the polynomial has one, two or three terms it is called a monomial, binomial or trinomial.
9 KB (1,497 words) - 10:44, 27 June 2015
...n be identified in a natural way with the ideals (cf. [[Ideal|Ideal]]) of $A$.
...ubstitute for unique factorization into prime factors if factorization in $A$ is not unique.
5 KB (853 words) - 12:16, 22 August 2014
$#A+1 = 137 n = 0
An algebra over a field for which certain polynomial identities are true.
15 KB (2,252 words) - 08:04, 6 June 2020
...the general case the local uniformization theorem implies the existence of a finite resolving system (see [[#References|[3]]]).
...align="top">[4]</TD> <TD valign="top"> O. Zariski, P. Samuel, "Commutative algebra" , '''2''' , Springer (1975) {{MR|0389876}} {{MR|0384768}} {{ZBL|0313.13001
3 KB (440 words) - 14:25, 1 May 2014
$#A+1 = 157 n = 0
...als, that is, in Artinian rings and algebras (cf. [[Artinian ring|Artinian ring]]), and that the description of Artinian semi-simple rings and algebras coi
16 KB (2,540 words) - 08:09, 6 June 2020
$#A+1 = 44 n = 0
$#C+1 = 44 : ~/encyclopedia/old_files/data/D033/D.0303680 Division algebra
5 KB (706 words) - 09:14, 28 June 2022
$#A+1 = 85 n = 4
$#C+1 = 85 : ~/encyclopedia/old_files/data/T092/T.0902240 Tate algebra
8 KB (1,161 words) - 08:25, 6 June 2020
...algebras]]; [[Jordan algebra|Jordan algebra]]; [[Mal'tsev algebra|Mal'tsev algebra]]).
...ive (Lie, special Jordan) algebra over a field can be imbedded in a simple algebra of the same type. In some classes of algebras there are many simple algebra
16 KB (2,433 words) - 21:48, 5 January 2016
An element $e_d$ of the group ring of the [[Symmetric group|symmetric group]] $S_m$ defined by the [[Young tab
...metrizer is that it is proportional to a primitive idempotent of the group algebra $\mathbf CS_m$. The coefficient of proportionality is equal to the product
961 bytes (180 words) - 13:01, 10 August 2014
...and $B$ be finite-dimensional algebras over a field $k$, and assume that $A$ is simple and $B$ is central simple (cf. also
[[Simple algebra|Simple algebra]];
4 KB (552 words) - 16:03, 26 April 2012