Maximal ideal
Maximal ideal In mathematics, more specifically in ring theory a maximal ideal is a special kind of ideal which is in some sense maximal, ...
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Talk:Maximal ideal
Talk:Maximal ideal I redirected this page and merged the ... links and none seemed to refer to ideal in order theory. MathMartin 11:18, 4 ... comment of mine after starting a new maximal ideal article with material from ideal (ring ...
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Prime ideal
Prime ideal In mathematics, a prime ideal is a subset of a ring which ... R is a commutative ring, then an ideal P of R is prime if it ... prime number if and only if the ideal nZ is a prime ideal in Z. Examples If R denotes ...
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Ideal (order theory)
Ideal (order theory) In mathematical order theory, an ideal is a special subset of a partially ... derived from the notion of a ring ideal of abstract algebra, it has subsequently been ... partially ordered set (P,≤) is an ideal, if the following conditions hold: For every ... the most general way to define an ideal for arbitrary posets, it was originally ...
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Principal ideal
Principal ideal In ring theory, a branch of abstract algebra, a principal ideal is an ideal I in a ring R that is ... of R. More specifically: a left principal ideal of R is a subset of R ... ra : r in R}; a right principal ideal is a subset of the form ...
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Ideal (ring theory)
Ideal (ring theory) In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal concept generalizes in an appropriate way some ... of arithmetic: in these rings, every nonzero ideal can be uniquely written as a product of prime ideals. An ideal can be used to construct a ...
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Boolean prime ideal theorem
Boolean prime ideal theorem In mathematics, a number of prime ideal theorems for guaranteeing the existence of certain ... of this form is the Boolean prime ideal theorem, which states that ideals in a ... of ring theory), or distributive lattices and maximal ideals (of order theory). This article currently focuses on prime ideal theorems from order theory. Although the ...
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Principal ideal domain
Principal ideal domain In abstract algebra, a principal ideal domain (PID) is an integral domain in which every ideal is principal (that is, generated by a ... a field. All Euclidean domains are principal ideal domains, but the converse is not true ... is not principal, since for example the ideal generated by 2 and X cannot ...
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Ideal class group
Ideal class group In mathematics the theory of ... group constructed from each such field, its ideal class group (or class group). The ideal class group measures the extent to which ... of K. History and origin of the ideal class group The first ideal class groups encountered in mathematics were ...
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Radical of an ideal
Radical of an ideal In ring theory, a branch of mathematics, the radical of an ideal is a kind of completion of the ideal. There are several special radicals associated with ... bad" properties of the ring. A radical ideal is an ideal that is its own radical (this ...
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