Last Updated：2025/11/21
Sentence
証明で構成された加群は、射影加群を射影部分加群で割った商であり、自己に対する Ext が 0 になり、有限個の直和の直和因子間の全射の核として右加群が存在するという性質を満たしている。
Quizzes for review
The tilting module constructed in the proof is a quotient of a projective module by a projective submodule, has Ext with itself equal to zero, and admits a right module as the kernel of a surjective morphism between finite direct sums of its direct summands.
See correct answer
The tilting module constructed in the proof is a quotient of a projective module by a projective submodule, has Ext with itself equal to zero, and admits a right module as the kernel of a surjective morphism between finite direct sums of its direct summands.
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Related words
tilting
Adjective
not-comparable
Japanese Meaning
数学（特に加群論）において、tilting とは、射影加群の部分からの射影加群による商として表現される加群であり、その加群自身との Ext 函手が 0 となる性質を持つ。また、有限個のその直和の部分からの全射写像の核として右加群が現れるという性質を有するものを指す。このような性質は、特定の変形（tilting）理論や対応関係の構築に利用される。
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