基本的和可伸缩的伽罗瓦连接
Essential and retractable Galois connections
摘要：
对于有界格，我们引入某些伽罗瓦连接，称为（循环）本质，可伸缩和UC伽罗瓦连接，这表现良好的概念，涉及本质性的模块理论性质。我们发现，基本可伸缩伽罗瓦连接保持一致的尺寸，而基本可伸缩UC伽罗瓦连接诱导一组封闭元素之间的双射对应。我们的结果适用于适当的伽罗瓦连接子模格之间。循环本质伽罗瓦联络统一了半投射模和半内射模，而可收缩伽罗瓦联络统一了可收缩模和可余收缩模。
英文摘要：
For bounded lattices, we introduce certain Galois connections, called (cyclically) essential, retractable and UC Galois connections, which behave well with respect to concepts of module-theoretic nature involving essentiality. We show that essential retractable Galois connections preserve uniform dimension, whereas essential retractable UC Galois connections induce a bijective correspondence between sets of closed elements. Our results are applied to suitable Galois connections between submodule lattices. Cyclically essential Galois connections unify semi-projective and semi-injective modules, while retractable Galois connections unify retractable and coretractable modules.
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