Finitely Valued f-Modules, An Addendum |
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Authors: | Stuart A Steinberg |
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Institution: | (1) Department of Mathematics, The University of Toledo, Toledo, Ohio, 43606, U.S.A. |
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Abstract: | In an -group M with an appropriate operator set it is shown that the -value set (M) can be embedded in the value set (M). This embedding is an isomorphism if and only if each convex -subgroup is an -subgroup. If (M) has a.c.c. and M is either representable or finitely valued, then the two value sets are identical. More generally, these results hold for two related operator sets 1 and 2 and the corresponding -value sets
and
. If R is a unital -ring, then each unital -module over R is an f-module and has
exactly when R is an f-ring in which 1 is a strong order unit. |
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Keywords: | lattice-ordered module value set |
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