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A [[Universal algebra|universal algebra]] which is a [[Group|group]] relative to the addition operation $ + $(
4 KB (643 words) - 08:01, 6 June 2020
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A commutative local ring to which the [[Hensel lemma|Hensel lemma]] applies, or, accordin
5 KB (787 words) - 22:10, 5 June 2020
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...mutative algebra|Commutative algebra]]) in which basic commutative algebra and [[Algebraic geometry|algebraic geometry]] can be performed. Zariski categor
4 KB (519 words) - 08:29, 6 June 2020
''group algebra of a group $G$ over a field $K$''
the [[Associative rings and algebras|associative algebra]] over $K$ whose elements are all possible finite sums of the type $\def\a{
5 KB (872 words) - 22:00, 29 April 2012
$#C+1 = 44 : ~/encyclopedia/old_files/data/D033/D.0303680 Division algebra
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5 KB (706 words) - 09:14, 28 June 2022
$#C+1 = 55 : ~/encyclopedia/old_files/data/M062/M.0602790 Matrix algebra,
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5 KB (738 words) - 08:00, 6 June 2020
''Associative rings and algebras'' are
rings and algebras with an associative multiplication, i.e., sets with
11 KB (1,726 words) - 20:09, 15 December 2020
...f. also [[PI-algebra]]) if there is a polynomial in the [[free associative algebra]] $\mathbf{Z}\langle x_1,x_2,\ldots\rangle$ which vanishes under all substi
...over a commutative ring satisfies the standard polynomial of degree $2n$, and no polynomial of lower degree.
4 KB (628 words) - 21:20, 11 December 2017
$#C+1 = 47 : ~/encyclopedia/old_files/data/P110/P.1100170 Poisson algebra
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8 KB (1,172 words) - 19:18, 17 March 2023
$#C+1 = 134 : ~/encyclopedia/old_files/data/I052/I.0502520 Involution algebra,
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9 KB (1,381 words) - 22:13, 5 June 2020
...algebras]]; [[Jordan algebra|Jordan algebra]]; [[Mal'tsev algebra|Mal'tsev algebra]]).
...ass of all algebras and in the class of all commutative (anti-commutative) algebras. For these classes, too, there holds an imbedding theorem analogous to that
16 KB (2,433 words) - 21:48, 5 January 2016
...inite-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
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and separable if $ \cap _ {n \in \mathbf Z } M _ {n} = 0 $.
3 KB (480 words) - 16:44, 13 January 2024
...a near-ring is a (not necessarily Abelian) group with respect to addition, and the right distributive property
...nalogue of a ring of matrices. The notions of a sub-near-ring, of an ideal and of a right module over a near-ring are introduced in the usual manner.
5 KB (767 words) - 11:23, 27 October 2014
...is a [[Ring|ring]] $R$ that is a [[Topological space|topological space]], and such that the mappings
and
3 KB (410 words) - 21:45, 23 July 2012
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...a unit element (cf. [[Associative rings and algebras]]) in which all right and left ideals are principal, i.e. have the form $ aR $
5 KB (880 words) - 19:00, 9 January 2024
$#C+1 = 40 : ~/encyclopedia/old_files/data/S086/S.0806210 Space over an algebra
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8 KB (1,172 words) - 16:55, 7 June 2020
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A theorem that describes all finite-dimensional associative real algebras without divisors of zero; it was proved by G. Frobenius [[#References|[1]]]
5 KB (790 words) - 19:40, 5 June 2020
$#C+1 = 70 : ~/encyclopedia/old_files/data/D033/D.0303860 Double and dual numbers
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6 KB (895 words) - 19:36, 5 June 2020
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be a commutative ring with unit, and let $ A $
4 KB (663 words) - 08:28, 20 January 2024