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A disjunctive syllogism is a valid argument form in propositional calculus, where p and q are propositions: (p v q; ¬p)/(∴q). For example, if someone is going to study law or ...

Let R be a number ring of degree n with 2s imaginary embeddings. Then every ideal class of R contains an ideal J such that ||J||<=(n!)/(n^n)(4/pi)^ssqrt(|disc(R)|), where ...

The set of nilpotent elements in a commutative ring is an ideal, and it is called the nilradical. Another equivalent description is that it is the intersection of the prime ...

Let R be a ring, and let I and J be ideals of R with I subset= J. Then J/I is an ideal of R/I and (R/I)/(J/I)=R/J.

A local ring is a ring R that contains a single maximal ideal. In this case, the Jacobson radical equals this maximal ideal. One property of a local ring R is that the subset ...

The probability law on the space of continuous functions g with g(0)=0, induced by the Wiener process.

The function defined by y=ab^(q^x). It is used in actuarial science for specifying a simplified mortality law (Kenney and Keeping 1962, p. 241). Using s(x) as the probability ...

A homogeneous ideal defining a projective algebraic variety is unmixed if it has no embedded prime divisors.

For any ideal I in a Dedekind ring, there is an ideal I_i such that II_i=z, (1) where z is a principal ideal, (i.e., an ideal of rank 1). Moreover, for a Dedekind ring with a ...

A logical structure which does not assume the law of the excluded middle. Three truth values are possible: true, false, or undecided. There are 3072 such logics.