...uence]] are Goursat congruences, the complete sequence consists of Goursat congruences.
Named after E. Goursat, who studied congruences of this type.
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The fully-characteristic congruences of an algebraic system $ A $
of all congruences of $ A $.
2 KB (267 words) - 19:40, 5 June 2020
...al surface of it (see [[#References|[1]]]). With every Laplace sequence of congruences there is associated a Laplace sequence of focal surfaces (see [[#References
2 KB (283 words) - 18:18, 24 December 2020
...re $a_i, b_i \in A$, $i=1,\ldots,n$, and $\omega$ is an $n$-ary operation. Congruences in algebraic systems are defined in a similar way. Thus, the equivalence cl
...lattice of relations is not a congruence. The product $\pi_1\pi_2$ of two congruences $\pi_1$ and $\pi_2$ is a congruence if and only if $\pi_1$ and $\pi_2$ comm
2 KB (277 words) - 22:08, 12 November 2016
...l surfaces of a Guichard congruence are called Guichard surfaces. Guichard congruences are named after G. Guichard (1889), who was the first to consider them.
...top"> G. Guichard, "Surfaces rapporteés à leurs lignes asymptotiques et congruences rapporteés à leurs développables" ''Ann. Sc. Ec. Norm. Sup. (3)'' , '''
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...face formed by a conjugate net of lines the tangents to which form two $W$-congruences — a so-called singular conjugate system. Only the Demoulin surfaces permi
...rojective deformation is related to $R$-congruences, which are special $W$-congruences (see [[#References|[a1]]] and [[#References|[2]]], [[#References|[3]]]).
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Examples of congruences: a $W$-congruence, in which the asymptotic lines on the focal surfaces corr
...Congruences of arbitrary lines (curves) in a space are called curvilinear congruences.
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...rrespond to each other by the orthogonality of the line elements, then the congruences formed by the rays passing through the points on $ S $
Such congruences were examined for the first time by A. Ribaucour in 1881.
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===Definition of $\Sigma$-congruences===
For a $\Sigma$-algebra $A$, the set $C(A)$ of all $\Sigma$-congruences for $A$ forms a complete [[Lattice|lattice]] w.r.t. set-theoretic inclusion
8 KB (1,264 words) - 16:16, 18 February 2013
...e correspondence with its normal subgroups, and the quotient groups by the congruences are the same as those by the normal subgroups. A quotient group is a normal
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c) there exists a family of congruences $ \rho _ {i} $,
such that the intersection of these congruences is the identity congruence and $ B/ \rho _ {i} \simeq A _ {i} $
3 KB (495 words) - 08:24, 6 June 2020
...on series of a universal algebra is defined in terms of congruences. Since congruences in groups are defined by normal subgroups, a composition series of a group
...\Omega$-algebra with subalgebra $E$ such that on any subalgebra of $A$ all congruences commute, then any two normal chains from $E$ to $A$ have isomorphic refinem
3 KB (566 words) - 14:25, 3 September 2017
...gebras]] with a non-trivial member contains also a member whose lattice of congruences is $2$-element. Such universal algebras are called congruence-simple or sim
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...h 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 modulo $ p $
elements. Congruences modulo a prime number can therefore be treated as equations over finite pri
7 KB (1,033 words) - 17:46, 4 June 2020
...ed. A commutative semi-group satisfies the minimum (maximum) condition for congruences if and only if it has a principal series and satisfies the minimum conditio
...I.B. Kozhukov, "On semigroups with minimal or maximal condition on left congruences" ''Semigroup Forum'' , '''21''' : 4 (1980) pp. 337–350</TD></TR><TR><
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are different prime numbers, is equivalent to the solvability of the congruences
is the number of solutions of (2). Thus, when studying congruences of the form (1) it is sufficient to confine oneself to moduli that are powe
4 KB (568 words) - 17:46, 4 June 2020
...modulus can be added, subtracted and multiplied in the same way as normal congruences. These operations induce similar operations on the residue classes modulo a
then for congruences modulo a double modulus, the analogue of the [[Fermat little theorem|Fermat
4 KB (700 words) - 18:53, 18 January 2024
...family $(q_\lambda)_{\lambda\in\Lambda}$ is called a separating family of congruences if the intersection of all the $q_\lambda$ is the diagonal congruence (the
3 KB (536 words) - 22:24, 26 October 2014
* N. Rama Rao, "Some congruences modulo $m$" ''Bull. Calcutta math. Soc.'' '''29''' (1938) 167-170 {{ZBL|64.
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...ical class. If in the definition of a radical the discussion is limited to congruences defined by ideals, then another concept of a radical arises, where the corr
the intersection of all congruences $ \theta $
5 KB (767 words) - 14:54, 7 June 2020