maximal ideal


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maximal ideal

[¦mak·sə·məl ī′dēl]
(mathematics)
An ideal I in a ring R which is not equal to R, and such that there is no ideal containing I and not equal to I or R.
References in periodicals archive ?
For a less trivial example, let M be a unique maximal ideal of a near-ring N with [M.
i+1)1] is a maximal ideal subspace of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and in general, [[?
is a maximal ideal chain in the ring ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]).
They proved two theorems as follow: In an ordered semigroup S, for which there exists an element a [member of] S such that the ideal of S generated by a is S, there is at most one maximal ideal which is the union of all proper ideals of S.
Kehayopulu,A note on minimal and maximal ideals of ordered semigroups, Lobachevskii Journal of Mathematics, 11:3-6, 1995.
The following result shows that every non-invertive left (right) TQ-algebra has dense maximal ideals.
Then A has all maximal ideals closed if and only if it is a Q-algebra.
Later Araujo ([1]) made a study of these maps in his thesis and has characterized Banach-Stone maps T , as those isometric isomorphisms which take invertible elements to invertible elements or maximal ideals to maximal ideals etc.
4) T maps maximal ideals of C(X) into maximal ideals of C(Y).
Later Araujo ([1]) made a study of these maps in his thesis and has characterized Banach-Stone maps T, as those isometric isomorphisms which take invertible elements to invertible elements or maximal ideals to maximal ideals etc.

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