Digit systems over commutative rings
2014 ◽
Vol 10
(06)
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pp. 1459-1483
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Keyword(s):
Modulo P
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Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be a polynomial. In the present paper we consider digit representations in the residue class ring [Formula: see text]. In particular, we are interested in the question whether each [Formula: see text] can be represented modulo P in the form e0 + e1x + ⋯ + ehxh, where the [Formula: see text] are taken from a fixed finite set of digits. This general concept generalizes both canonical number systems and digit systems over finite fields. Due to the fact that we do not assume that 0 is an element of the digit set and that P need not be monic, several new phenomena occur in this context.
2009 ◽
Vol 147
(1)
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pp. 9-29
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Keyword(s):
2019 ◽
Vol 1176
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pp. 042019
Keyword(s):
1999 ◽
Vol 42
(3)
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pp. 621-640
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Keyword(s):
Keyword(s):
1961 ◽
Vol 57
(3)
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pp. 483-488
Keyword(s):
1987 ◽
Vol 43
(2)
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pp. 171-175
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