ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXIV, 1 (2005)
p. 49 - 58
On the fragmental structures
M. A. Kamal and N. S. Mahmoud
Abstract.
In this work we study the fragment structures over a ring extension $R$ of a
ring $R_{0}$. The defining conditions of the fragments with the partial
actions on the descending chains of $R_{0}$-modules measure how far they
are from being \hbox{$R$-modules}. The category of $R$-fragments lies between the
categories of $R_{0}$-modules and of \hbox{$R$-modules}. Inspite of $R$-fragments,
in a general setting, are far from being \hbox{$R$-modules}; they behave, in some
ways, the same as $R$-modules. We prove some imprtant results for finitely
spanned fragments and some of their related properties.
AMS Subject classification: 15A87.
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