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The Pierce Decomposition And Pierce Embedding Of Endomorphism Rings Of Abelian P-Groups, Brendan Goldsmith, Luigi Salce
The Pierce Decomposition And Pierce Embedding Of Endomorphism Rings Of Abelian P-Groups, Brendan Goldsmith, Luigi Salce
Articles
We prove that more classes of groups than those described by Pierce have the property that the map Ψ is surjective, and we furnish examples of groups which do not have this property. Several results connecting the Pierce decomposition and the Pierce embedding of End(G) are obtained that allow one to derive general conditions on a group G which ensure that the Pierce embedding of End(G) is not surjective.
On Adjoint Entropy Of Abelian Groups, Brendan Goldsmith, Ketao Gong
On Adjoint Entropy Of Abelian Groups, Brendan Goldsmith, Ketao Gong
Articles
The theory of endomorphism rings of algebraic structures allows, in a natural way, a systematic approach based on the notion of entropy borrowed from dynamical systems. In the present work we introduce a \lq dual\rq \ notion based upon the replacement of the finite groups used in the definition of algebraic entropy, by subgroups of finite index. The basic properties of this new entropy are established and a connection to Hopfian groups is investigated.
Algebraic Entropy For Abelian Groups, Dikran Dikranjan, Brendan Goldsmith, Luigi Salce, Paolo Zanardo
Algebraic Entropy For Abelian Groups, Dikran Dikranjan, Brendan Goldsmith, Luigi Salce, Paolo Zanardo
Articles
The theory of endomorphism rings of algebraic structures allows, in a natural way, a systematic approach based on the notion of entropy borrowed from dynamical systems. Here we study the algebraic entropy of the endomorphisms of Abelian groups, introduced in 1965 by Adler, Konheim and McAndrew. The so-called Addition Theorem is proved; this expresses the algebraic entropy of an endomorphism $ \phi$ of a torsion group as the sum of the algebraic entropies of the restriction to a $ \phi$-invariant subgroup and of the endomorphism induced on the quotient group. Particular attention is paid to endomorphisms with zero algebraic entropy …
Describing Ideals Of Endomorphism Rings, Brendan Goldsmith, Simone Pabst
Describing Ideals Of Endomorphism Rings, Brendan Goldsmith, Simone Pabst
Articles
No abstract available.
Realising Rings As Endomorphism Rings: The Impact Of Logic, Brendan Goldsmith
Realising Rings As Endomorphism Rings: The Impact Of Logic, Brendan Goldsmith
Articles
No abstract available
Endomorphism Rings Of Torsion-Free Modules Over A Complete Discret Valuation Ring., Brendan Goldsmith
Endomorphism Rings Of Torsion-Free Modules Over A Complete Discret Valuation Ring., Brendan Goldsmith
Articles
No abstract available.