...m was first obtained by J. Wedderburn for finite-dimensional algebras over a field, and was proved by E. Artin [[#References|[1]]] in its final formulat
...Artin, "The influence of J.H.M. Wedderburn on the development of modern algebra" ''Bull. Amer. Math. Soc.'' , '''56''' (1950) pp. 65–72</TD></TR>
1 KB (211 words) - 06:17, 13 September 2016
A topological ring is a [[Ring|ring]] $R$ that is a [[Topological space|topological space]], and such that the mappings
...gical ring. A direct product of topological rings is a topological ring in a natural way.
3 KB (410 words) - 21:45, 23 July 2012
$#A+1 = 15 n = 0
$#C+1 = 15 : ~/encyclopedia/old_files/data/K055/K.0505930 Krull ring,
3 KB (424 words) - 22:15, 5 June 2020
$#A+1 = 47 n = 0
$#C+1 = 47 : ~/encyclopedia/old_files/data/E036/E.0306760 Excellent ring
4 KB (643 words) - 19:38, 5 June 2020
$#A+1 = 29 n = 0
$#C+1 = 29 : ~/encyclopedia/old_files/data/S083/S.0803900 Self\AAhinjective ring,
4 KB (550 words) - 08:13, 6 June 2020
$#A+1 = 57 n = 0
$#C+1 = 57 : ~/encyclopedia/old_files/data/H046/H.0406940 Hensel ring
5 KB (787 words) - 22:10, 5 June 2020
An ideal in a ring or algebra that is not a [[Prime ideal|prime ideal]].
72 bytes (15 words) - 17:06, 7 February 2011
$#A+1 = 36 n = 0
''of a ring''
5 KB (764 words) - 08:09, 6 June 2020
$#A+1 = 37 n = 0
$#C+1 = 37 : ~/encyclopedia/old_files/data/P072/P.0702750 Place of a field
2 KB (326 words) - 08:06, 6 June 2020
...ain modules if and only if $R$ is a generalized [[Uniserial ring|uniserial ring]].
...a$-uniserial are used for a direct sum of uniserial modules (respectively, a finite direct sum of uniserial modules).
751 bytes (111 words) - 16:40, 1 May 2014
$#A+1 = 27 n = 0
$#C+1 = 27 : ~/encyclopedia/old_files/data/N066/N.0606850 Noetherian ring,
3 KB (539 words) - 18:51, 3 April 2024
''unique factorisation domain'', ''Gaussian ring''
...irreducible elements $P$ such that every non-zero element $a\in A$ admits a unique representation
3 KB (480 words) - 21:45, 3 January 2021
...ising the properties of a [[Lie algebra]]. A Leibniz algebra $L$ is a $K$-algebra with multiplication denoted by $[\cdot,\cdot]$ satisfying
Every [[Lie algebra]] is a Leibniz algebra, and a Leibniz algebra is a Lie algebra if in addition $[x,x] = 0$.
1 KB (217 words) - 15:05, 19 November 2023
$#A+1 = 9 n = 0
$#C+1 = 9 : ~/encyclopedia/old_files/data/S091/S.0901020 Subrepresentation of a representation
812 bytes (117 words) - 08:24, 6 June 2020
A non-zero [[unital module]] $M$ over a [[unital ring]] $R$ that contains only two submodules: the null module and $M$ itself.
...]]s of $G$ over $K$ are precisely the irreducible modules over the [[group algebra]] $R = k[G]$.
2 KB (391 words) - 18:11, 18 March 2018
$#A+1 = 21 n = 0
A left (or right) module $ M $
2 KB (372 words) - 19:39, 5 June 2020
...algebraic operations on tensors (cf. [[Tensor on a vector space|Tensor on a vector space]]) are studied.
...r a commutative associative ring $A$ with unit is the algebra $T(V)$ over $A$ whose underlying module has the form
2 KB (329 words) - 04:49, 23 July 2018
$#A+1 = 33 n = 0
$#C+1 = 33 : ~/encyclopedia/old_files/data/D030/D.0300550 Dedekind ring
4 KB (637 words) - 17:32, 5 June 2020
$#A+1 = 18 n = 0
A generalization of the notion of an associative ring (cf. [[Associative rings and algebras|Associative rings and algebras]]). Le
3 KB (408 words) - 08:11, 6 June 2020
''of a closed symmetric algebra $R$ of bounded linear operators on a Hilbert space $H$''
A commutative symmetric Banach algebra $E$ of operators on $H$ such that $(R\cup E)'=E$. Diagonal algebras are emp
2 KB (264 words) - 11:41, 26 March 2023