Geodesic
On the smallest and the largest elements of the Lockett section of a fitting functor
Problemy fiziki, matematiki i tehniki, no. 1 (2012), pp. 69-74.

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In the paper analogues of the known in the theory of Fitting classes operators «$^*$», «$_ *$ » and the Lockett sections on the set of Fitting $\mathfrak{X}$-functors ($\mathfrak{X}$ is some non-empty Fitting class) are defined. By the Lockett section of a conjugate Fitting $\mathfrak{X}$-functor $f$ we mean the set $\mathrm{Locksec}(f) = \{g: g\text{ is a conjugate Fitting }\mathfrak{X}\text{-functor and }f^* = g^*\}$. It is proved that the Lockett section of a conjugate Fitting $\mathfrak{X}$-functor contains the largest element. Besides we describe conditions under which the Lockett section contains the smallest element.
Keywords: Lockett's operation, Lockett section, Fitting $\mathfrak{X}$-functor. 
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     url = {http://geodesic.mathdoc.fr/item/PFMT_2012_1_a12/}
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E. A. Vit'ko. On the smallest and the largest elements of the Lockett section of a fitting functor. Problemy fiziki, matematiki i tehniki, no. 1 (2012), pp. 69-74. http://geodesic.mathdoc.fr/item/PFMT_2012_1_a12/

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