different between maximal vs semilocal

English

Etymology

maximum +? -al

Adjective

maximal

1. Largest, greatest (in magnitude), highest, most.

Abbreviations

• max.

Synonyms

• maximum (adj)

Antonyms

• minimal

Derived terms

• halfmaximal
• submaximal
• supermaximal

Translations

Noun

maximal (plural maximals)

1. (mathematics) The element of a set with the greatest magnitude.
2. (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).
3. (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 ?, the set contains either ? or ~?.

Synonyms

• maximum

References

• maximal on Wikipedia.Wikipedia

French

Etymology

From maximum +? -al.

Adjective

maximal (feminine singular maximale, masculine plural maximaux, feminine plural maximales)

1. maximal

Related terms

• maximum
• max
• maxi

Further reading

• “maximal” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

German

Pronunciation

• Rhymes: -a?l

Adjective

maximal (not comparable)

1. maximal

Declension

Antonyms

• minimal

Further reading

• “maximal” in Duden online

Interlingua

Adjective

maximal (not comparable)

1. maximal

Romanian

Etymology

From French maximal

Adjective

maximal m or n (feminine singular maximal?, masculine plural maximali, feminine and neuter plural maximale)

1. maximal

Declension

Spanish

Adjective

maximal (plural maximales)

1. maximal

Swedish

Adjective

maximal (comparative maximalare, superlative maximalast)

1. maximal; as large as possible

Declension

Antonyms

• minimal

English

Alternative forms

• semi-local

Etymology

semi- +? local

Adjective

semilocal (not comparable)

1. (mathematics) Describing a ring that has a finite number of maximal ideals