...ate cases, may be reduced to the problem of the number of solutions of the congruences $ F ( x _ {1} \dots x _ {n} ) \equiv 0 $(
in one variable are the two-term congruences (cf. [[Two-term congruence|Two-term congruence]])
8 KB (1,148 words) - 17:46, 4 June 2020
...in projective differential geometry are: the (projective) theory of linear congruences (cf. [[Congruence in geometry|Congruence in geometry]]), and problems on [[
...ack to the end of the 19th century; the work of G. Darboux on surfaces and congruences was especially important. The first book in which classical projective diff
6 KB (838 words) - 08:08, 6 June 2020
...on an algebra $\mathbf{A}$ which is expressible as the intersection of all congruences on $\mathbf{A}$ whose factor algebras belong to some fixed variety of $\Ome
1 KB (167 words) - 19:23, 12 December 2015
...cobson objects, i.e., objects whose prime congruences are meets of maximal congruences. Jacobson categories are axiomatically defined as categories $ \mathbf A
3 KB (517 words) - 22:14, 5 June 2020
Bianchi congruences were studied by L. Bianchi [[#References|[1]]].
1 KB (216 words) - 16:33, 19 October 2014
...edekind lattice is a modular lattice. If a universal algebra has commuting congruences, then its congruence lattice is a complete Dedekind lattice [[#References|[
2 KB (231 words) - 17:45, 4 June 2020
6) for any finite sequence of co-disjunctable congruences $ r _ {1} \dots r _ {n} $
denotes union of congruences on $ A $
4 KB (519 words) - 08:29, 6 June 2020
Congruences modulo one and the same number can be added, subtracted and multiplied in t
The operations of addition, subtraction and multiplication of congruences induce similar operations on the residue classes. Thus, if $ a $
20 KB (3,011 words) - 09:59, 26 March 2023
...en Gödelization and coordinatization can be extended to [[Sigma-Congruence|congruences]] defined on $A$ and $C$. A congruence $\sim^\beta \subseteq A \times A$ i
2 KB (241 words) - 07:50, 21 March 2023
...References|[a5]]]) to a graphical representation of the plactic, or Knuth, congruences.
The plactic (or Knuth) congruences are the following: Let the alphabet $X$ be totally ordered and suppose that
5 KB (732 words) - 20:14, 9 November 2023
...$p(n)$ (see [[#References|[a1]]]) and Ramanujan discovered the surprising congruences $p(5m+4) \equiv 0 \pmod 5$, $p(7m+5) \equiv 0 \pmod 7$, $p(11m+6) \equiv 0
2 KB (231 words) - 15:33, 11 November 2023
...haracterized by all the conics in the congruence belonging to one quadric. Congruences of conics whose planes form a one-parameter family have one quadruplicate f
are the most general one-parameter families, congruences and complexes of conics in $ P _ {3} $.
8 KB (1,191 words) - 06:39, 9 April 2023
A [[Semi-group|semi-group]] not containing proper ideals or congruences of some fixed type. Various kinds of simple semi-groups arise, depending on
...ne of which is the null class; and congruence-free semi-groups, not having congruences other than the universal relation and the equality relation.
8 KB (1,074 words) - 18:06, 1 June 2023
...ible to calculate the Legendre symbol easily, without resorting to solving congruences. For example,
2 KB (339 words) - 18:03, 19 December 2014
...ar the ideals, and also on certain relations on semi-groups, in particular congruences. Such restrictions give rise, for example, to various types of simple semi-
...n completely $0$-simple semi-groups, and the far-reaching investigation of congruences on inverse semi-groups; the theory of radicals of semi-groups (cf. [[Radica
17 KB (2,435 words) - 09:18, 2 April 2023
congruence if all its classes are convex subsets; the kernel congruences of $ o $-
congruences. The decomposition of a totally ordered semi-group $ S $
11 KB (1,676 words) - 14:07, 17 March 2020
The conformal-differential geometry in the plane studies sequences and congruences of circles. To a sequence of circles corresponds a curve in three-dimension
...riants of the associated surface in hyperbolic space, and special types of congruences are singled out.
6 KB (942 words) - 17:46, 4 June 2020
...he semi-group, in particular, the behaviour of $E$ with respect to certain congruences. There exists on any inverse semi-group $S$ a least congruence $\sigma$ wit
7 KB (986 words) - 19:33, 2 January 2018
The validity of the following congruences has been demonstrated:
Certain congruences have also been proved , [[#References|[13]]] for odd $ n $.
16 KB (2,200 words) - 08:30, 14 January 2024
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2 KB (327 words) - 14:23, 15 April 2023