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**unique****factorization****domain**, called UFD for short, is any integral**domain**in which every nonzero noninvertible element has a**unique****factorization**, i.e., an essentially ...In an integral

**domain**R, the decomposition of a nonzero noninvertible element a as a product of prime (or irreducible) factors a=p_1...p_n, (1) is**unique**if every other ...The term

**domain**has (at least) three different meanings in mathematics. The term**domain**is most commonly used to describe the set of values D for which a function (map, ...The property of being the only possible solution (perhaps modulo a constant, class of transformation, etc.).

The determination of a set of factors (divisors) of a given integer ("prime factorization"), polynomial ("polynomial factorization"), etc., which, when multiplied together, ...

A principal ideal

**domain**is an integral**domain**in which every proper ideal can be generated by a single element. The term "principal ideal domain" is often abbreviated P.I.D. ...A Reinhardt

**domain**with center c is a**domain**D in C^n such that whenever D contains z_0, the**domain**D also contains the closed polydisk.A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral

**domain**.Evans et al. (2000, p. 6) use the unfortunate term "probability domain" to refer to the range of the distribution function of a probability density function. For a continuous ...

Let G be a group and S be a topological G-set. Then a closed subset F of S is called a fundamental

**domain**of G in S if S is the union of conjugates of F, i.e., S= union _(g ......