Geodesic
Rank of formal matrix. System of formal linear equations. Zero divisors
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 52 (2018), pp. 5-12

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In this paper, we present the notion of the formal rank, i.e., the rank of a formal matrix over an arbitrary commutative ring, and some its general properties. Next, we introduce the notion of systems of formal linear equations and give necessary and sufficient conditions for the existence of a solution of homogenous systems of formal linear equations. In Section 2, we show that Cramer's rule is still valid for systems of formal linear equations. Finally, in Section 3, we establish the condition under which a formal matrix is a left or right zero divisor.
Keywords: ring, rank of formal matrix, system of formal linear equations.
Mots-clés : formal matrix 
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     author = {T. D. Norbosambuev},
     title = {Rank of formal matrix. {System} of formal linear equations. {Zero} divisors},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {5--12},
     publisher = {mathdoc},
     number = {52},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2018_52_a0/}
}
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T. D. Norbosambuev. Rank of formal matrix. System of formal linear equations. Zero divisors. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 52 (2018), pp. 5-12. http://geodesic.mathdoc.fr/item/VTGU_2018_52_a0/