Geodesic
Artinian bimodule with quasi-Frobenius bimodule of translations
Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 70-91.

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The possibility to generalize the notion of a linear recurrent sequence (LRS) over a commutative ring to the case of a LRS over a non-commutative ring is discussed. In this context, an arbitrary bimodule $_AM_B$ over left- and right-Artinian rings $A$ and $B$, respectively, is associated with the equivalent bimodule of translations $_CM_Z$, where $C$ is the multiplicative ring of the bimodule $_AM_B$ and $Z$ is its center, and the relation between the quasi-Frobenius conditions for the bimodules $_AM_B$ and $_CM_Z$ is studied. It is demonstrated that, in the general case, the fact that $_AM_B$ is a quasi-Frobenius bimodule does not imply the validity of the quasi-Frobenius condition for the bimodule $_CM_Z$. However, under some additional assumptions it can be shown that if $_CM_Z$ is a quasi-Frobenius bimodule, then the bimodule $_AM_B$ is quasi-Frobenius as well. } \keywords{ Quasi-Frobenius bimodule, Artinian ring, multiplicative ring, bimodule of translatios, linear recurrent sequence
Keywords: Quasi-Frobenius bimodule, Artinian ring, multiplicative ring, bimodule of translatios, linear recurrent sequence. 
@article{DM_2017_29_3_a5,
     author = {A. A. Nechaev and V. N. Tsypyschev},
     title = {Artinian bimodule with {quasi-Frobenius} bimodule of translations},
     journal = {Diskretnaya Matematika},
     pages = {70--91},
     publisher = {mathdoc},
     volume = {29},
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     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2017_29_3_a5/}
}
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A. A. Nechaev; V. N. Tsypyschev. Artinian bimodule with quasi-Frobenius bimodule of translations. Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 70-91. http://geodesic.mathdoc.fr/item/DM_2017_29_3_a5/

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