scholarly journals Analytic and arithmetic theory of semigroups with divisor theory

1992 ◽  
Vol 4 (2) ◽  
pp. 199-238 ◽  
Author(s):  
Alfred Geroldinger ◽  
Jerzy Kaczorowski
Keyword(s):  
Divisor Theory ◽  
Arithmetic Theory

scholarly journals Finding large Selmer rank via an arithmetic theory of local constants

2007 ◽  
Vol 166 (2) ◽  
pp. 579-612 ◽  
Author(s):  
Barry Mazur ◽  
Karl Rubin
Keyword(s):  
Arithmetic Theory

scholarly journals Some Theorems On Matrices With Real Quaternion Elements

1955 ◽  
Vol 7 ◽  
pp. 191-201 ◽  
Author(s):  
N. A. Wiegmann
Keyword(s):  
Similarity Transformation ◽  
Elementary Divisor ◽  
Quaternion Matrix ◽  
Unitary Similarity ◽  
Triangular Form ◽  
Quaternion Matrices ◽  
Divisor Theory ◽  
Real Quaternion ◽  
Unitary Similarity Transformation

Matrices with real quaternion elements have been dealt with in earlier papers by Wolf (10) and Lee (4). In the former, an elementary divisor theory was developed for such matrices by using an isomorphism between n×n real quaternion matrices and 2n×2n matrices with complex elements. In the latter, further results were obtained (including, mainly, the transforming of a quaternion matrix into a triangular form under a unitary similarity transformation) by using a different isomorphism.

The nullity of a wild knot in a compact 3-manifold

1973 ◽  
Vol 16 (3) ◽  
pp. 262-271
Author(s):  
James M. McPherson
Keyword(s):  
Fundamental Group ◽  
Present Author ◽  
Elementary Divisor ◽  
Divisor Theory ◽  
Infinitely Generated Modules ◽  
Torsion Free

The nullity of the Alexander module of the fundamental group of the complement of a knot in S3 was one of the invariants of wild knot type defined and investigated by E. J. Brody in [1], in which he developed a generalised elementary divisor theory applicable to infinitely generated modules over a unique factorisation domain. Brody asked whether the nullity of a knot with one wild point was bounded above by its enclosure genus; for knots in S3, the present author showed in [6] that this was indeed the case. In [7], it was (prematurely) stated by the author that this was also the case for knots k embedded in a 3-manifold M so that H,(M — k) was torsion-free.

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