In mathematics|lang=en terms the difference between maximal and semilocal
is that maximal is (mathematics) said of an ideal of a ring or a filter of a lattice : that it is as large as it can be without being trivial (improper) while semilocal is (mathematics) describing a ring that has a finite number of maximal ideals.
As adjectives the difference between maximal and semilocal
is that maximal is largest, greatest (in magnitude), highest, most while semilocal is (mathematics) describing a ring that has a finite number of maximal ideals.
As a noun maximal
is (mathematics) the element of a set with the greatest magnitude.
maximal
English
Adjective
(head)
Largest, greatest (in magnitude), highest, most.
Antonyms
* minimal
Derived terms
* submaximal
Noun
(
en noun)
(mathematics) The element of a set with the greatest magnitude.
(mathematics) Said of an ideal of a ring or a filter of a lattice : that it is as large as it can be without being trivial (improper).
(logic) Said of a set of well-formed formulas'': that it is as large as it can be without being inconsistent; i.e. that for any well-formed formula ''φ'', the set contains either ''φ'' or ~''φ .
Synonyms
* maximum
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semilocal
English
Alternative forms
* semi-local
Adjective
(Semi-local ring)
(-)
(mathematics) Describing a ring that has a finite number of maximal ideals