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1
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On a theorem of Tate

100%
Bogomolov F., Tschinkel Y.
Open Mathematics
|
2008
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tom 6
|
nr 3
343-350
EN
We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.
2
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A variation of zero-divisor graphs

100%
Gupta R., Sen M., Ghosh S.
Discussiones Mathematicae - General Algebra and Applications
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2015
|
tom 35
|
nr 2
159-176
EN
In this paper, we define a new graph for a ring with unity by extending the definition of the usual 'zero-divisor graph'. For a ring R with unity, Γ₁(R) is defined to be the simple undirected graph having all non-zero elements of R as its vertices and two distinct vertices x,y are adjacent if and only if either xy=0 or yx=0 or x+y is a unit. We consider the conditions of connectedness and show that for a finite commutative ring R with unity, Γ₁(R) is connected if and only if R is not isomorphic to ℤ₃ or $ℤ₂^k$ (for any k ∈ ℕ-{1}\). Then we characterize the rings R for which Γ₁(R) realizes some well-known classes of graphs, viz., complete graphs, star graphs, paths (i.e., $P_n$), or cycles (i.e., $C_n$). We then look at different graph-theoretical properties of the graph Γ₁(F), where F is a finite field. We also find all possible Γ₁(R) graphs with at most 6 vertices.
3
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Continued fractions of Laurent series with partial quotients from a given set

88%
Lauder A.
Acta Arithmetica
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1999
|
tom 90
|
nr 3
251-271
4
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An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field

63%
Abad M., Díaz Varela J., López Martinolich B., C. Vannicola M., Zander M.
Open Mathematics
|
2006
|
tom 4
|
nr 4
547-561
EN
In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L p,k, and the finite field F(p k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L p,k) generated by L p,k into the variety V(F(p k)) generated by F(p k) and an interpretation Φ2 of V(F(p k)) into V(L p,k) such that Φ2Φ1(B) = B for every B ε V(L p,k) and Φ1Φ2(R) = R for every R ε V(F(p k)).
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