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Title of Journal: J Math Sci

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Abbravation: Journal of Mathematical Sciences

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Springer US

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DOI

10.1007/bf02238257

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1573-8795

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Algebraic Representation of Mappings Between Submo

Authors: U Brehm
Publish Date: 2013/08/07
Volume: 193, Issue: 3, Pages: 388-393
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Abstract

We discuss algebraic representations of mappings preserving arbitrary joins between submodule lattices For a given joinpreserving mapping bargmathfrakLleft RM rightto mathfrakLleft SN right between submodule lattices a representation is an Rbalanced mapping h B × M → N where S B R is a bimodule such that leftlangle hleft Btimes U right rightrangle =bargU for all Uin mathfrakLleft RM right We begin by posing the question in a general abstract context and by defining the canonical subrepresentation which is a representation if and only if there exists a representation The problem is to give easy and natural conditions for the existence of a representation We consider a very general situation for the mappings and give sufficient criteria for the existence of a representation We also consider lattice isomorphisms

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