Maximal element
Maximal element In mathematics, especially in order theory, a maximal element of a subset S of some partially ordered set is an element of S that is not smaller ...
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Maximum element   (translated from French)
Maximum element Definition In one ensemble ordered , one maximum element such as there is an element is not any other element of this unit which is higher to him. Dualement, one defines minimal element : element such as there is not ...
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Maximal
Maximal Maximal has several meanings: Maximal element, a mathematical definition. Maximal, a faction of Transformers. This is ...
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Maximal subgroup
Maximal subgroup In mathematics, the term maximal subgroup is used to mean slightly different ... areas of algebra. In group theory, a maximal subgroup H of a group G is ... strictly. In other words H is a maximal element of the partially ordered set of ...
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Greatest element
Greatest element In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set (poset) is an element of S which is greater than or equal to any other element of S. The term least element is defined dually. A bounded poset ...
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Algebraic element   (translated from Spanish)
Algebraic element One or more wikipedistas they are working ... of main ideals, all prime ideal is maximal, with which $(p)$ it is ideal maximal of $K[x]$, soon . An element is algebraic on a body if and ...
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Glossary of ring theory
... of R. Types of elements Central An element r of a ring R is central ... as the center of R. Idempotent An element e of a ring is idempotent if e 2 = e. Irreducible An element x of a ring is irreducible if ... but not necessarily vice versa. Prime An element x of a ring is prime if ... a or x divides b. Nilpotent An element r of R is nilpotent if ...
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Glossary of order theory
... atom in a poset P with least element 0, is an element that is minimal among all elements that ... 0. A atomic poset P with least element 0 is one in which, for every non-zero element x of P, there is an atom ... algebra is a distributive lattice with least element 0 and greatest element 1, in ...
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Zorn's lemma
... an upper bound contains at least one maximal element. It is named after the mathematician Max ... ∈ T. Note that u is an element of P but need not be an element of T. A maximal element of P is an element ...
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Supremum
... an ordered set S is the least element that is greater than or equal to each element of S. Consequently, it is also referred ... set S. If S contains a greatest element, then that element is the supremum; and if not, then ... immediately clear what it means for an element to be "greater-or-equal" than ...
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