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An affine algebraic group over a field k is a representable covariant functor from the category of commutative algebras over k to the category of groups such that the representing algebra is finitely generated.
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Vocabulary list

karada
noun
  1. body (からだ is a gikun reading of 身体)
  2. torso; trunk
  3. build; physique; frame; figure
  4. health; constitution
  5. corpse; dead body
ue
noun, no adjective, adverb, noun, used as a suffix
  1. above; up; over; elder (e.g. daughter)
noun
  1. top; summit; head (e.g. of a staircase)
  2. surface
noun, no adjective, adverb
  1. before; previous
noun, no adjective
  1. superiority; one's superior; one's elder
noun, adverb
  1. on top of that; besides; what's more; not only ... but (following a verb or adjective)
  2. upon (further inspection, etc.); based on (and occurring after) (following a verb or noun)
  3. matters concerning ...; as concerns ...
  4. since (i.e. "for that reason") (as ~上は)
noun, used as a suffix
  1. honorable; venerable (suffix indicating higher social standing than the speaker)
  2. place of one's superior (e.g. the throne)
  3. emperor; sovereign; shogun; daimyo
  4. noblewoman (esp. the wife of a nobleman)
no
particle
  1. indicates possessive (occasionally ん, orig. written 乃 or 之)
  2. nominalizes verbs and adjectives
  3. substitutes for "ga" in subordinate phrases
  4. (at sentence-end, falling tone) indicates a confident conclusion (often ん)
  5. (at sentence-end) indicates emotional emphasis
  6. (at sentence-end, rising tone) indicates question
daisuu
noun, no adjective
  1. algebra
noun
  1. number of generations (e.g. in imperial succession)
gun
noun, noun, used as a suffix
  1. group; bunch; crowd; throng; swarm; band
  2. group
toha
expression, particle
  1. indicates word or phrase being defined
  2. used for quoting (thoughts, speech, etc.) (indicates contrast or adds emphasis to a negative statement)
  3. with (more emphatic than と)
  4. (not) as much as; (not) so much as (with neg. verb)
  5. the fact that; to think that; such a thing as (indicates surprise, disbelief, anger, etc.; sometimes at sentence end)
to
particle, conjunction
  1. if; when
  2. and
particle
  1. with
  2. used for quoting (thoughts, speech, etc.)
noun
  1. promoted pawn
particle
  1. indicates a question (at sentence end)
ha
particle
  1. topic marker particle (pronounced わ in modern Japanese)
  2. indicates contrast with another option (stated or unstated)
  3. adds emphasis
ue
noun, no adjective, adverb, noun, used as a suffix
  1. above; up; over; elder (e.g. daughter)
noun
  1. top; summit; head (e.g. of a staircase)
  2. surface
noun, no adjective, adverb
  1. before; previous
noun, no adjective
  1. superiority; one's superior; one's elder
noun, adverb
  1. on top of that; besides; what's more; not only ... but (following a verb or adjective)
  2. upon (further inspection, etc.); based on (and occurring after) (following a verb or noun)
  3. matters concerning ...; as concerns ...
  4. since (i.e. "for that reason") (as ~上は)
noun, used as a suffix
  1. honorable; venerable (suffix indicating higher social standing than the speaker)
  2. place of one's superior (e.g. the throne)
  3. emperor; sovereign; shogun; daimyo
  4. noblewoman (esp. the wife of a nobleman)
no
particle
  1. indicates possessive (occasionally ん, orig. written 乃 or 之)
  2. nominalizes verbs and adjectives
  3. substitutes for "ga" in subordinate phrases
  4. (at sentence-end, falling tone) indicates a confident conclusion (often ん)
  5. (at sentence-end) indicates emotional emphasis
  6. (at sentence-end, rising tone) indicates question
ka
noun, noun, used as a suffix
  1. acceptable; satisfactory; allowed; permitted
noun
  1. approval; being in favour; (a) vote in favour; aye
  2. Pass (grade); Fair; C; D (on a 優, 良, 可 scale)
moto
noun
  1. origin; source (usu. 元)
  2. base; basis; foundation; root (esp. 基)
  3. cause (also 因, 原)
  4. ingredient; material (esp. 素)
  5. (somebody's) side; (somebody's) location
  6. original cost (or capital, principal, etc.)
  7. (plant) root; (tree) trunk
  8. first section of a waka
counter
  1. counter for blades of grass, tree trunks, etc., and for falcons (in falconry)
noun
  1. handle (chopsticks, brush, etc.); grip
moto
no adjective, noun, used as a prefix
  1. former; ex-; past; one-time
noun, no adjective
  1. earlier times; the past; previous state
noun, adverb
  1. formerly; previously; originally; before
tamaki
noun
  1. bracelet (made of stringed jewels or bells and worn at the elbow)
  2. bracer (for the elbow of an archer)
no
particle
  1. indicates possessive (occasionally ん, orig. written 乃 or 之)
  2. nominalizes verbs and adjectives
  3. substitutes for "ga" in subordinate phrases
  4. (at sentence-end, falling tone) indicates a confident conclusion (often ん)
  5. (at sentence-end) indicates emotional emphasis
  6. (at sentence-end, rising tone) indicates question
ken
suffix
  1. sphere; circle; range; area; zone; bloc
noun
  1. category
kara
particle
  1. from (e.g. time, place, numerical quantity); since
  2. from (originator); by
  3. because; since (follows verbs, adjectives)
  4. out of (constituent, part)
  5. through (e.g. window, vestibule)
  6. after; since (following the te-form of a verb)
  7. expresses sympathy or warning
gun
noun, noun, used as a suffix
  1. group; bunch; crowd; throng; swarm; band
  2. group
no
particle
  1. indicates possessive (occasionally ん, orig. written 乃 or 之)
  2. nominalizes verbs and adjectives
  3. substitutes for "ga" in subordinate phrases
  4. (at sentence-end, falling tone) indicates a confident conclusion (often ん)
  5. (at sentence-end) indicates emotional emphasis
  6. (at sentence-end, rising tone) indicates question
ken
suffix
  1. sphere; circle; range; area; zone; bloc
noun
  1. category
he
particle
  1. to; towards; for (indicates direction or goal; pronounced え in modern Japanese)
no
particle
  1. indicates possessive (occasionally ん, orig. written 乃 or 之)
  2. nominalizes verbs and adjectives
  3. substitutes for "ga" in subordinate phrases
  4. (at sentence-end, falling tone) indicates a confident conclusion (often ん)
  5. (at sentence-end) indicates emotional emphasis
  6. (at sentence-end, rising tone) indicates question
hyougen
noun, suru verb
  1. expression; presentation
  2. representation; notation
kanou
na adjective, noun
  1. possible; potential; practicable; feasible
na
particle
  1. don't (prohibitive; used with dictionary form verb)
  2. do (imperative (from なさい); used with -masu stem of verb)
interjection
  1. hey; listen; you
particle
  1. now, ...; well, ...; I tell you!; you know (when seeking confirmation, for emphasis, etc.; used at sentence end)
  2. wow; ooh (used to express admiration, emotionality, etc.; used at sentence end)
domo
suffix
  1. first-person plural (or singular)
  2. second or third person plural (implies speaker is of higher status than those referred to)
tomo
noun, noun, used as a prefix
  1. together with
  2. same
suffix
  1. both; all; neither; none
  2. including ...
goto
suffix
  1. including...; with ...; inclusive of; ...and all
muta
mita
noun
  1. together with ... (after noun+が, pronoun+の, etc.)
hen
na adjective, noun
  1. strange; odd; peculiar; weird; curious; queer; eccentric; funny; suspicious; fishy
  2. unexpected
  3. change
  4. incident; disturbance; disaster; accident
noun, used as a prefix
  1. flat
kanshu
noun
  1. functor
seki
noun, noun, used as a suffix
  1. barrier; gate
noun
  1. seki (in go); mutual life (usu. セキ)
te
noun
  1. hand; arm (occ. pronounced た when a prefix)
  2. forepaw; foreleg
  3. handle
  4. hand; worker; help
  5. trouble; care; effort
  6. means; way; trick; move; technique; workmanship
  7. hand; handwriting
  8. kind; type; sort
  9. one's hands; one's possession
  10. ability to cope
  11. hand (of cards)
  12. direction
noun, noun, used as a suffix, counter
  1. move (in go, shogi, etc.)
de
particle
  1. at; in (indicates location of action; にて is the formal literary form)
  2. at; when (indicates time of action)
  3. by; with (indicates means of action)
conjunction
  1. and then; so
auxiliary
  1. and; then (indicates continuing action; alternative form of 〜て used for some verb types)
particle
  1. let me tell you; don't you know (at sentence-end; indicates certainty, emphasis, etc.)
yuugenseisei
noun or verb acting prenominally
  1. finitely generated; of finite type
yuugen
no adjective, na adjective, noun
  1. finite; limited
seisei
noun, suru verb
  1. creation; generation; formation; derivation
na
particle
  1. don't (prohibitive; used with dictionary form verb)
  2. do (imperative (from なさい); used with -masu stem of verb)
interjection
  1. hey; listen; you
particle
  1. now, ...; well, ...; I tell you!; you know (when seeking confirmation, for emphasis, etc.; used at sentence end)
  2. wow; ooh (used to express admiration, emotionality, etc.; used at sentence end)
tagen
noun, no adjective
  1. pluralism; diversity
tamaki
noun
  1. bracelet (made of stringed jewels or bells and worn at the elbow)
  2. bracer (for the elbow of an archer)
niyotte
expression
  1. according to; by (means of); due to; because of
niyoru

te-form

niyotte
expression, godan verb
  1. by means of; due to; because of; according to
hyougen
noun, suru verb
  1. expression; presentation
  2. representation; notation
suru

Passive Plain Present Indicative Form

sareru
suru verb (irregular)
  1. to do; to carry out; to perform
  2. to cause to become; to make (into); to turn (into)
  3. to serve as; to act as; to work as
  4. to wear (clothes, a facial expression, etc.)
  5. to judge as being; to view as being; to think of as; to treat as; to use as (as 〜にする,〜とする)
  6. to decide on; to choose (as 〜にする)
suru verb (irregular), intransitive verb
  1. to be sensed (of a smell, noise, etc.) (as 〜がする)
  2. to be (in a state, condition, etc.)
  3. to be worth; to cost
  4. to pass (of time); to elapse
suru verb (irregular), transitive verb
  1. to place, or raise, person A to a post or status B (as AをBにする)
  2. to transform A to B; to make A into B; to exchange A for B (as AをBにする)
  3. to make use of A for B; to view A as B; to handle A as if it were B (as AをBにする)
  4. to feel A about B (as AをBにする)
suffix, suru verb (irregular)
  1. verbalizing suffix (applies to nouns noted in this dictionary with the part of speech "vs")
auxiliary verb, suru verb (irregular)
  1. creates a humble verb (after a noun prefixed with "o" or "go")
  2. to be just about to; to be just starting to; to try to; to attempt to (as 〜うとする,〜ようとする)

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