Results 51 to 60 of about 131,023 (367)

The Diophantine equation ax2+2bxy−4ay2=±1

International Journal of Mathematics and Mathematical Sciences, 2003
We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation ax2+2bxy−4ay2=±1, where a and b are nonnegative integers.
Lionel Bapoungué
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Algebraic relations among Goss’s zeta values on elliptic curves

Forum of Mathematics, Sigma, 2023
In 2007 Chang and Yu determined all the algebraic relations among Goss’s zeta values for $A=\mathbb F_q[\theta ]$ , also known as the Carlitz zeta values.
Nathan Green, Tuan Ngo Dac
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On Generation of the Group $PGL_n(\mathbb{Z}+i\mathbb{Z})$ by Three Involutions, Two of which Commute

Известия Иркутского государственного университета: Серия "Математика"
The results of the paper relate to the following general problem. Find natural finite generating  sets of elements of a given linear group over a finitely generated commutative ring.
Ya.N. Nuzhin, T. B. Shaipova
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On periodic rings

International Journal of Mathematics and Mathematical Sciences, 2001
It is proved that a ring is periodic if and only if, for any elements x and y, there exist positive integers k,l,m, and n with either k≠m or l≠n, depending on x and y, for which xkyl=xmyn. Necessary and sufficient conditions are established for a ring to
Xiankun Du, Qi Yi
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On equivalence of pairs of matrices, which determinants are primes powers, over quadratic Euclidean rings

Karpatsʹkì Matematičnì Publìkacìï, 2013
We establish that a pair of matrices, which determinants are primes powers, can  be reduced over quadratic Euclidean ring $\mathbb{K}=\mathbb{Z}[\sqrt{k}]$ to their triangular forms with invariant factors on a main diagonal by using the common ...
N.B. Ladzoryshyn
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On Mertens-Ces\`aro Theorem for Number Fields

, 2015
Let $K$ be a number field with ring of integers $\mathcal O$. After introducing a suitable notion of density for subsets of $\mathcal O$, generalizing that of natural density for subsets of $\mathbb Z$, we show that the density of the set of coprime $m ...
Ferraguti, Andrea, Micheli, Giacomo
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Cube-root-subgroups of SL2 over imaginary quadratic integers [PDF]

Computer Science Journal of Moldova, 2021
All cube roots of the identity in the special linear group of $2\times 2$-matrices with entries in the ring of integers in $\mathbb Q[\sqrt{d}]$ are described.
Miroslav Kures
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Torsion homology of arithmetic lattices and K2 of imaginary fields

, 2013
We study upper bounds for the torsion in homology of nonuniform arithmetic lattices. Together with recent results of Calegari-Venkatesh, this can be used to obtain upper bounds on K2 of the ring of integers of totally imaginary fields.Comment: Version 2 ...
Emery, Vincent
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Characteristic free description of semi-invariants of $2\times 2$ matrices [PDF]

, 2019
A minimal homogeneous generating system of the algebra of semi-invariants of tuples of two-by-two matrices over an infinite field of characteristic two or over the ring of integers is given.
Domokos, M.
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Modules over group rings of groups with restrictions on the system of all proper subgroups [PDF]

International Journal of Group Theory, 2015
We consider the class M of R{modules where R is an associative ring. Let A be a module over a group ring RG, G be a group and let L(G) be the set of all proper subgroups of G. We suppose that if H 2 L(G) then A=CA(H) belongs to M. We study an RG{module A
Olga Dashkova
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