Quotient group
Quotient group In mathematics, given a group G ... a normal subgroup N of G, the quotient group, or factor group, of G over ... subgroup N to the identity element. The quotient group is written G/N and is ... of all subsets of G forms a monoid under this operation. In terms of this ... operation we can first explain what a quotient group is, and then explain what ...
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Syntactic monoid
Syntactic monoid In mathematics, the syntactic monoid M(L) of a formal language L ... an alphabet A is defined as the quotient M(L) = A * / ~ L , where ~ L denotes ... It can be shown that the syntactic monoid of L is the smallest monoid that recognizes L; that is, M( ...
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Quotient category
Quotient category In mathematics, a quotient category is a category obtained from another ... notion is similiar to that of a quotient group or quotient space, but in the categorical setting. Definition ... R on C we can define the quotient category C/R as the category ...
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Kernel (algebra)
... taking various forms, that applies to the quotient algebra defined by the kernel. In this ... it makes sense to speak of the quotient space V/(ker T). The first isomorphism ... theorem for vector spaces states that this quotient space is naturally isomorphic to the image ... it makes sense to speak of the quotient group G/(ker f). The first isomorphism theorem for groups states that this quotient group is naturally isomorphic to the ...
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Group action
... as X/G, and is called the quotient of the action; in geometric situations it ... left cosets of G x . The standard quotient theorem of set theory then gives a ... compatible with the action of G. The quotient X/G inherits the quotient topology from X, and is called the quotient space of the action. The above ...
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User:Omegatron/Prettytable examples
... under the operation of division, since the quotient of two integers (e.g., 1 divided ... that Z under multiplication is a commutative monoid. However, note that not every integer has ... process can be mimicked to form the quotient field of any integral domain, where an ... under the operation of division, since the quotient of two integers (e.g., 1 divided ... that Z under multiplication is a commutative monoid. However, note that not every integer ...
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Group (mathematical)   (translated from French)
... algebraic structure of one group is one monoid all the elements are invertible; i.e ... maths>. One can then make the following quotient \frac G \mathcal R, noted ... makes it possible to define the group quotient \frac Z {n\mathbb Z} is distinguished and the quotient is isomorphous with the group \frac ... G|}{|H|}=2) is distinguished and quotient groups it is then isomorphous with < ...
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Adjoint functors
... implication in propositional logic, or the ideal quotient for division by ring ideals, can be ... From monoids and groups to rings The monoid ring construction gives a functor from monoids ... to a given ring its underlying multiplicative monoid. Similarly, the group ring construction yields a ... the category of rings, to get the monoid and group rings over K. Direct and ... on a topological space has a commutative monoid structure under direct sum. To make ...
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Glossary of mathematical attributes   (translated from German)
... in $\backslash mathfrak\; g\_k$ its), their quotient abelsch is. degenerated One bilineare Illustration b ... 0 , if the limes of the difference quotient in the place x 0 existed. Dimension ... are free Gruppoid , free half-group , free Monoid , free group, free abelsche group. Module is ... zero divisor-free and completelocked in its Quotient body is or this condition for all ... not normal, the whole conclusion in the quotient body $\backslash mathbb\; Q(\backslash sqrt5)$ ...
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Dyck language
... By treating Σ ∗ as an algebraic monoid under concatenation we see that the monoid structure transfers onto the quotient Σ ∗ /R, resulting in the syntactic monoid of the Dyck language. The class Cl ... ε) will be denoted 1. The syntactic monoid of the Dyck language is not ...
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