论文标题
复杂功能代数的投射烦恼和隐居性
Projective freeness and Hermiteness of complex function algebras
论文作者
论文摘要
论文研究了复杂值连续功能在拓扑空间，Stein代数和交换性的Unital Banach代数上的复杂值连续功能的代数的遗体。给出了代数的最大理想空间上的新的足够的共同体条件，以保证实现这些特性。结果通过非平凡的例子说明了结果。基于Borsuk的形状理论，引入了新的类$ \ Mathscr {C} $的交换性班克代数的$ \ MATHSCR {C} $（在可交换代数中的本地戒指类似），以便投影式启动产品与代数的tensor tensor tensor in代数在$ \ mathscr c $ Presserves Practive Practive Practive Practive Practive projective projective projective。 $ \ Mathscr {C} $以及其他投影免费和HERMITE功能代数代数代数的一些示例已组装。其中包括例如道格拉斯代数，对称函数的代数有限生成的代数，BOHR-WIENER代数，霍明型半完全周期函数的代数和界定全体形态函数的代数。
The paper studies projective freeness and Hermiteness of algebras of complex-valued continuous functions on topological spaces, Stein algebras, and commutative unital Banach algebras. New sufficient cohomology conditions on the maximal ideal spaces of the algebras are given that guarantee the fulfilment of these properties. The results are illustrated by nontrivial examples. Based on the Borsuk theory of shapes, a new class $\mathscr{C}$ of commutative unital complex Banach algebras is introduced (an analog of the class of local rings in commutative algebra) such that the projective tensor product with algebras in $\mathscr C$ preserves projective freeness and Hermiteness. Some examples of algebras of class $\mathscr{C}$ and of other projective free and Hermite function algebras are assembled. These include, e.g., Douglas algebras, finitely generated algebras of symmetric functions, Bohr-Wiener algebras, algebras of holomorphic semi-almost periodic functions, and algebras of bounded holomorphic functions on Riemann surfaces.
