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Full-Text Articles in Mathematics
Torsion-Free Groups And Modules With The Involution Property, Brendan Goldsmith, C. Meehan, S.L. Wallutis
Torsion-Free Groups And Modules With The Involution Property, Brendan Goldsmith, C. Meehan, S.L. Wallutis
Articles
An Abelian group or module is said to have the involution property if every endomorphism is the sum of two automorphisms, one of which is an involution. We investigate this property for completely decomposable torsion-free Abelian groups and modules over the ring of -adic integers.
Unit Sum Numbers Of Abelian Groups And Modules, Christopher Meehan
Unit Sum Numbers Of Abelian Groups And Modules, Christopher Meehan
Doctoral
We discuss some open questions regarding the unit sum numbers of free modules of arbitrary infinite rank over commutative rings and, in particular, over principal ideal domains. The unit sum numbers of rational groups are then investigated: the importance of the rational prime 2 being an automorphism of the rational group is discussed and other results are achieved considering the number and distribution of rational primes which are, or are not, automorphisms of the group. We next prove the existence of rational groups with unit sum numbers greater than 2 but of finite value and we estimate an upper bound …