Geodesic
Multiplicative orders on terms
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 101-107

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Let $R$ be a commutative ring with identity. Any order on terms of the polynomial algebra $R[x_1,\dots,x_k]$ induces in a natural way the notion of a leading term. An order on terms is called multiplicative if and only if the leading term of a product equals the product of leading terms. In this paper, we present a procedure for the construction of multiplicative orders. We obtain some characterizations of rings for which such orders exist. We give conditions sufficient for the existence of such orders. 
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     author = {E. V. Gorbatov},
     title = {Multiplicative orders on terms},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {101--107},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_1_a5/}
}
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E. V. Gorbatov. Multiplicative orders on terms. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 101-107. http://geodesic.mathdoc.fr/item/FPM_2007_13_1_a5/