Notre Dame Journal of Formal Logic

Deissler Rank Complexity of Powers of Indecomposable Injective Modules

R. Chartrand and T. Kucera


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.

Article information

Notre Dame J. Formal Logic, Volume 35, Number 3 (1994), 398-402.

First available in Project Euclid: 21 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]
Secondary: 13C11: Injective and flat modules and ideals


Chartrand, R.; Kucera, T. Deissler Rank Complexity of Powers of Indecomposable Injective Modules. Notre Dame J. Formal Logic 35 (1994), no. 3, 398--402. doi:10.1305/ndjfl/1040511345.

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