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Cite Details

Rick Chartrand and Thomas Kucera, "Deissler rank complexity of powers of indecomposable injective modules", Notre Dame J. Formal Logic, vol. 35, pp. 398--402, 1994


Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of first-order structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we solve a problem of the second author by showing that certain injective envelopes have the maximum possible positive Deissler rank complexity. The proof shows that this complexity naturally reflects the internal structure of the injective extension in the form of the levels of the Matlis hierarchy.

BibTeX Entry

author = {Rick Chartrand and Thomas Kucera},
title = {Deissler rank complexity of powers of indecomposable injective modules},
year = {1994},
urlpdf = {http://math.lanl.gov/Research/Publications/Docs/chartrand-1994-deissler.pdf},
journal = {Notre Dame J. Formal Logic},
volume = {35},
pages = {398--402}