Abstract
Let D be a commutative domain which is not a field. Then, in general, there exist a lot of indecomposable D-modules. Between them completely anisotropic seem to be the most pathological. Examples of such modules were known only over principal ideal domains with many maximal ideals. These examples were torsion-free of rank two.
In this note we are going to construct completely anisotropic modules, of rank not only two, over unique factorization domains having many irreducible elements. Our examples are applicable to near-rings of homogeneous maps of modules.
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© 1997 Kluwer Academic Publishers
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Krempa, J. (1997). Some Examples of Indecomposable Modules. In: Saad, G., Thomsen, M.J. (eds) Nearrings, Nearfields and K-Loops. Mathematics and Its Applications, vol 426. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1481-0_22
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DOI: https://doi.org/10.1007/978-94-009-1481-0_22
Publisher Name: Springer, Dordrecht
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