AI 中文总结
本文建立了具有近一致项的代数的全局表示统一理论，刻画了相关最优结果，其技术核心是Baker–Pixley定理同余系统分量的无穷扩展。
AI 中文摘要
全局表示是满足类似层状局部到全局拼接原理的次直表示。我们建立了这类表示的统一简化理论。对于具有近一致项的拟簇，该框架通过统一论证恢复了主要经典表示定理，并得到了有界次直宽度因子的一般表示。当相对次直不可约元构成通用类时，我们得到最优结果：每个相对同余分配代数都允许由相对全局不可分解因子构成的全局表示，我们对该因子进行了明确刻画。我们还给出了逆命题：有界相对次直宽度因子的全局表示强制近一致项存在。在主定理假设中加入半单性，得到滤子拟簇和双鉴别器簇的最优表示结果，同时给出全局不可分解代数的简单刻画。这些结果背后的技术核心是Baker–Pixley定理同余系统分量的新无穷扩展。
英文摘要
Global representations are subdirect representations satisfying a sheaf-like local-to-global patching principle. We develop a unified and simplified theory of such representations. For quasivarieties with a near-unanimity term, this framework recovers the main classical representation theorems through a common argument and yields a general representation by factors of bounded subdirect width. When the relatively subdirectly irreducible members form a universal class, we obtain an optimal result: every relatively congruence-distributive algebra admits a global representation by relatively globally indecomposable factors, which we characterize explicitly. We also provide a converse: global representations by factors of bounded relative subdirect width force the existence of a near-unanimity term. Adding semisimplicity to the hypotheses of the main theorem yields optimal representation results for filtral quasivarieties and dual discriminator varieties, together with a simple description of the globally indecomposable algebras. The technical engine behind these results is a new infinitary extension of the congruence-system component of the Baker--Pixley theorem.
