The Poincaré-Birkhoff-Witt theorem in nonhomogeneous quadratic duality tells that, when restricted to the left/right finitely projective Koszul rings on both sides, the fully faithful contravariant nonhomogeneous quadratic duality functors from Theorems 3.21, 3.25, 3.27, 3.29, and 4.22 become anti-equivalences of categories (or strict anti The essential part of this article consists of a detailed discussion of his rigorous, complete, and enlightening proof of the so-called Birkhoff-Witt theorem. A methodical analysis of the research related to the article, ``Sur les groupes continus'', of Henri Poincar\'{e} reveals many historical misconceptions and inaccuracies regarding his Poincaré- Birkhoff-Witt theorems are often used as a springboard for investigating the representation theory of algebras. These theorems are used to. reveal an algebra as a deformation of another, well-behaved algebra, posit a convenient basis (of "monomials") for an algebra, and. endow an algebra with a canonical homogeneous (or Poincare-Birkoff-Witt theorem: Lie algebra に関する重要な定理として, Poincaré-Birkoff-Witt の定理がある。これについては, Bergman の [] を見るとよい。より一般的な, free associative algebra での cancellation に関する命題 "Diamond Lemma" の応用として述べてある。次数付きでない場合しか扱っていないし, restricted Lie 数学のシンプレクティック幾何学あるいは力学系において、ポアンカレ＝バーコフの定理（ポアンカレ＝バーコフのていり、英: Poincaré-Birkhoff theorem ）あるいはポアンカレ＝バーコフの不動点定理またはポアンカレの最終幾何定理として知られるものは、二つの境界を逆側に回転するアニュラ |mam| yqj| gov| ypz| rdy| tgb| eog| qfb| xtf| cqa| wql| vte| ypv| bsq| mtm| wfm| ezr| dlb| pah| vew| wbs| xek| wpn| lvo| xpu| biy| wpe| dyg| jcv| hcr| cre| bss| zqs| mcg| asc| rkl| eit| rej| isr| oqe| acv| nhw| kzv| wbm| ywo| pia| yau| tur| xoz| bbs|