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Ring sizes can be measured physically by a paper, plastic, or metal ring sizer (as a gauge) or by measuring the inner diameter of a ring that already fits. Ring sticks are tools used to measure the inner size of a ring, and are typically made from plastic, delrin, wood, aluminium, or of multiple materials. Digital ring sticks can be used for ...
For any division ring D and positive integer n, the matrix ring M n (D) is semisimple (and simple). For a field k and finite group G, the group ring kG is semisimple if and only if the characteristic of k does not divide the order of G (Maschke's theorem). Clifford algebras are semisimple. The Weyl algebra over a field is a simple ring, but it ...
The free ring , …, plays the role of the coordinate ring of the affine space in the noncommutative algebraic geometry (i.e., we don't demand free variables to commute) and thus a generic matrix ring of size n is the coordinate ring of a noncommutative affine variety whose points are the Spec's of matrix rings of size n (see below for a more ...
Formally, the polynomial ring in n noncommuting variables with coefficients in the ring R is the monoid ring R[N], where the monoid N is the free monoid on n letters, also known as the set of all strings over an alphabet of n symbols, with multiplication given by concatenation. Neither the coefficients nor the variables need commute amongst ...
A heterocyclic compound or ring structure is a cyclic compound that has atoms of at least two different elements as members of its ring(s). [1] Heterocyclic organic chemistry is the branch of organic chemistry dealing with the synthesis, properties, and applications of organic heterocycles .
A cyclic compound (or ring compound) is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring. Rings may vary in size from three to many atoms, and include examples where all the atoms are carbon (i.e., are carbocycles), none of the atoms are carbon (inorganic cyclic ...
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