Hopkins–Levitzki theorem
In the branch of abstract algebra called ring theory, the Akizuki–Hopkins–Levitzki theorem connects the descending chain condition and ascending chain condition in modules over semiprimary rings. A ring R (with 1) is called semiprimary if R/J(R) is semisimple and J(R) is a nilpotent ideal, where J(R) denotes the Jacobson radical. The theorem states that if R is a semiprimary ring and M is an R module, the three module conditions Noetherian, Artinian and "has a composition series" are equivalent. Without the semiprimary condition, the only true implication is that if M has a composition series, then M is both Noetherian and Artinian.
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Hopkins–Levitzki theorem
In the branch of abstract algebra called ring theory, the Akizuki–Hopkins–Levitzki theorem connects the descending chain condition and ascending chain condition in modules over semiprimary rings. A ring R (with 1) is called semiprimary if R/J(R) is semisimple and J(R) is a nilpotent ideal, where J(R) denotes the Jacobson radical. The theorem states that if R is a semiprimary ring and M is an R module, the three module conditions Noetherian, Artinian and "has a composition series" are equivalent. Without the semiprimary condition, the only true implication is that if M has a composition series, then M is both Noetherian and Artinian.
has abstract
Charles Hopkins の論文と Jacob Lev ...... アルティン環であることと左ネーター環であることは同値である。
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In the branch of abstract alge ...... only if it is left Noetherian.
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29,435,296
Wikipage revision ID
701,499,401
comment
Charles Hopkins の論文と Jacob Lev ...... アルティン環であることと左ネーター環であることは同値である。
@ja
In the branch of abstract alge ...... both Noetherian and Artinian.
@en
label
Hopkins–Levitzki theorem
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ホプキンス・レヴィツキの定理
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