Abstract
In the paper, two classes of involutive divisions related to admissible monomial orderings--?-divisions and ?-divisions--are considered. The latter may be viewed as an improvement of the class of induced divisions introduced in [1]. The continuity and constructivity of the ?-divisions, as well as a number of additional properties of the ?-divisions, are proved. Taking into account that the Janet division is a ?-division associated with the lexicographical order, its "antipode"--a ?-division associated with the same order--is separated in the class of the ?-divisions.
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