...rentiation: differential rings, differential modules, differential fields, and differential algebraic varieties.
...of the main objects of differential algebra is the algebra of differential polynomials $ {\mathcal F} \{ Y _{1} \dots Y _{n} \} $ ,
30 KB (4,468 words) - 18:44, 17 December 2019
Please remove this comment and the {{TEX|auto}} line below,
and satisfies the relation usually referred to as the [[Leibniz rule]]
6 KB (945 words) - 17:32, 5 June 2020
...the theory of field extensions (cf. [[Extension of a field|Extension of a field]]). Let $ K $
be some extension of a field $ k $ .
6 KB (793 words) - 17:24, 17 December 2019
Please remove this comment and the {{TEX|auto}} line below,
and equality $ \mathop{\rm rk} L = \mathop{\rm dim} L $
3 KB (460 words) - 08:09, 6 June 2020
...tive algebraic groups [[#References|[4]]], [[#References|[5]]], and in the theory of formal groups [[#References|[6]]]. Let $ A $
which are added and multiplied in accordance with the following rules: $$
17 KB (2,502 words) - 17:25, 22 December 2019
If the TeX and formula formatting is correct, please remove this message and the {{TEX|semi-auto}} category.
...stance, if $K \subseteq L$ is a field extension (cf. also [[Extension of a field]]), then $L$ is a Fatou extension of $K$.
5 KB (828 words) - 11:51, 24 December 2020
$#C+1 = 48 : ~/encyclopedia/old_files/data/R077/R.0707310 Random field, generalized,
Please remove this comment and the {{TEX|auto}} line below,
7 KB (970 words) - 08:09, 6 June 2020
Please remove this comment and the {{TEX|auto}} line below,
and endowing $ U ^ {*} $,
8 KB (1,190 words) - 08:16, 20 January 2024
Please remove this comment and the {{TEX|auto}} line below,
of modules and any homomorphism $ \beta : P \rightarrow C $
7 KB (1,080 words) - 08:08, 6 June 2020
...nd numerical; for example, in the (numerical) solution of linear equations and eigenvalue problems. A few well-known factorizations are listed below.
...th $m\ge n$ over $\C$. Then there exist a unitary $(m\times m)$-matrix $Q$ and a right-triangular $m\times n$-matrix $R$ such that $A=QR$. Here, a right-t
9 KB (1,294 words) - 22:47, 28 February 2015
''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
and the solution to this equation may be obtained by using
Ferro's result; he also solved the equation $x^3+px+q$ ($(p>0$, $q>0$), and
2 KB (312 words) - 19:38, 15 March 2023
Please remove this comment and the {{TEX|auto}} line below,
...ce in which the modulus is a prime number. A distinguishing feature of the theory of congruences modulo a prime number is the fact that the residue classes m
7 KB (1,033 words) - 17:46, 4 June 2020
...articular, in a ring of polynomials in a finite number of variables over a field or over a ring of integers any ideal is generated by a finite number of ele
be an irreducible polynomial over the field $ \mathbf Q $
18 KB (2,720 words) - 19:17, 19 December 2019
a linear algebraic group over some field, related to a semi-simple
Chevalley basis of the algebra $\fg$, and let $\fg_\Z$ be its linear
6 KB (1,002 words) - 19:25, 3 November 2013
A [[Differential field|differential field]] $ F \supset F _{0} $
and $ F _{0} $;
13 KB (1,981 words) - 20:02, 17 December 2019
...among the widely available systems is REDUCE, which runs on many platforms and is still being further developed.
...1983. Maple was released in 1986, while Scratchpad II (later called AXIOM) and Mathematica appeared by 1988.
9 KB (1,315 words) - 06:33, 4 June 2024
...ring, there exists a one-to-one correspondence between varieties of rings and the $T$-ideals of a countably-generated free ring. If for two varieties of
...bra with a finite number of generators over a field of characteristic zero and if $M_2\not\subseteq\mathfrak M$, then $\mathfrak M$ is a Specht variety.
4 KB (701 words) - 17:01, 23 November 2023
$#C+1 = 70 : ~/encyclopedia/old_files/data/D033/D.0303860 Double and dual numbers
Please remove this comment and the {{TEX|auto}} line below,
6 KB (895 words) - 19:36, 5 June 2020
Please remove this comment and the {{TEX|auto}} line below,
of polynomials over a field $ F $,
4 KB (576 words) - 19:42, 5 June 2020