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Also called Macaulay ring, a Cohen Macaulay ring is a Noetherian commutative unit ring R in which any proper ideal I of height n contains a sequence x_1, ..., x_n of elements ...

The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...

One of the operations of addition, subtraction, multiplication, division, and integer (or rational) root extraction.

The lattice method is an alternative to long multiplication for numbers. In this approach, a lattice is first constructed, sized to fit the numbers being multiplied. If we ...

The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

A mathematical object S is said to be additively closed if a,b in S implies that a+b in S.

When ac is divisible by a number b that is relatively prime to a, then c must be divisible by b.

A mathematical object S is said to be multiplicatively closed if a,b in S implies that ab in S.

An operator * for which a*b=-b*a is said to be anticommutative.

A relation R on a set S is transitive provided that for all x, y and z in S such that xRy and yRz, we also have xRz.