Notre Dame Journal of Formal Logic

Deissler Rank Complexity of Powers of Indecomposable Injective Modules

R. Chartrand and T. Kucera

Abstract

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

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

Dates
First available in Project Euclid: 21 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040511345

Digital Object Identifier
doi:10.1305/ndjfl/1040511345

Mathematical Reviews number (MathSciNet)
MR1326121

Zentralblatt MATH identifier
0840.03026

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

Citation

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. https://projecteuclid.org/euclid.ndjfl/1040511345


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References

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