Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Daniel Smertnig"'
Autor:
Daniel Smertnig, John Voight
Publikováno v:
Transactions of the London Mathematical Society, Vol 6, Iss 1, Pp 53-86 (2019)
Abstract We enumerate all orders in definite quaternion algebras over number fields with the Hermite property; this includes all orders with the cancellation property for locally free modules.
Externí odkaz:
https://doaj.org/article/a274ab5e3c314a2b83c5eb1b3bae1258
Autor:
Jason Bell, Daniel Smertnig
Publikováno v:
Canadian Journal of Mathematics. :1-35
A multivariate, formal power series over a field K is a Bézivin series if all of its coefficients can be expressed as a sum of at most r elements from a finitely generated subgroup $G \le K^*$ ; it is a Pólya series if one can take $r=1$ . We give
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ae438a416fbdb3bc8d462af1a2d13db2
https://doi.org/10.4153/s0008414x22000517
https://doi.org/10.4153/s0008414x22000517
Publikováno v:
Journal of the European Mathematical Society.
We study the asymptotic growth of coefficients of Mahler power series with algebraic coefficients, as measured by their logarithmic Weil height. We show that there are five different growth behaviors, all of which being reached. Thus, there are \emph
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04dd2f0b7053ac090affcb7def0d2154
https://doi.org/10.4171/jems/1244
https://doi.org/10.4171/jems/1244
A ring has bounded factorizations if every cancellative nonunit $a \in R$ can be written as a product of atoms and there is a bound $\lambda(a)$ on the lengths of such factorizations. The bounded factorization property is one of the most basic finite
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b9d9fada94761f85ea1b38f85e003844
Autor:
Jason P. Bell, Daniel Smertnig
Publikováno v:
Selecta Mathematica. 27
A (noncommutative) Pólya series over a fieldKis a formal power series whose nonzero coefficients are contained in a finitely generated subgroup of$$K^\times $$K×. We show that rational Pólya series are unambiguous rational series, proving a 40 yea
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::92cc2f4a5163de28653db8a95eb41a94
https://doi.org/10.1007/s00029-021-00629-2
https://doi.org/10.1007/s00029-021-00629-2
Autor:
Daniel Smertnig, Nicholas R. Baeth
We study direct-sum decompositions of torsion-free, finitely generated modules over a (commutative) Bass ring $R$ through the factorization theory of the corresponding monoid $T(R)$. Results of Levy-Wiegand and Levy-Odenthal together with a study of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::50914c3368df35b3c7bbeea32fa22d3c
Autor:
John Voight, Daniel Smertnig
Publikováno v:
Transactions of the London Mathematical Society, Vol 6, Iss 1, Pp 53-86 (2019)
We enumerate all orders in definite quaternion algebras over number fields with the Hermite property; this includes all orders with the cancellation property for locally free modules.
Comment: Some typos corrected; final version; 24 pages plus t
Comment: Some typos corrected; final version; 24 pages plus t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fd2214c4888862cda8ac855950374d28
Autor:
Daniel Smertnig
Publikováno v:
Transactions of the American Mathematical Society. 369:2477-2491
A classical result of Claborn states that every abelian group is the class group of a commutative Dedekind domain. Among noncommutative Dedekind prime rings, apart from PI rings, the simple Dedekind domains form a second important class. We show that
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fd78b142b7bafb54e639d115d67d79a8
https://doi.org/10.1090/tran/6868
https://doi.org/10.1090/tran/6868
Autor:
Nicholas R. Baeth, Daniel Smertnig
Publikováno v:
Journal of Algebra. 441:475-551
We study the non-uniqueness of factorizations of non zero-divisors into atoms (irreducibles) in noncommutative rings. To do so, we extend concepts from the commutative theory of non-unique factorizations to a noncommutative setting. Several notions o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89c9f2d6bf9e90c100df26c6624e45c7
https://doi.org/10.1016/j.jalgebra.2015.06.007
https://doi.org/10.1016/j.jalgebra.2015.06.007
Locally acyclic cluster algebras are Krull domains. Hence their factorization theory is determined by their (divisor) class group and the set of classes containing height-1 prime ideals. Motivated by this, we investigate class groups of cluster algeb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::054f73b290a577d08e1728da787d7315
http://arxiv.org/abs/1712.06512
http://arxiv.org/abs/1712.06512