Split Decomposition over an Abelian Group Part 1: Generalities

Split decomposition over an abelian group, Part 2: Group-valued split systems with weakly compatible support

Split-decomposition theory deals with relations between R-valued split systems and metrics. In a previous publication (the first of a series of papers on split decomposition over an abelian group), a general conceptual framework has been set up to study these relationships from an essentially algebraic point of view, replacing metrics by certain more general, appropriately definedmultivariatema...

متن کامل

Phylogenetic Diversity Over an Abelian Group

There is a natural way to associate to any tree T with leaf set X , and with edges weighted by elements from an abelian group G, a map from the power set of X into G — simply add the elements on the edges that connect the leaves in that subset. This map has been wellstudied in the case where G has no elements of order 2 (particularly when G is the additive group of real numbers) and, for this s...

متن کامل

MODULES OVER A PID A module over a PID is an abelian group

A module over a PID is an abelian group that also carries multiplication by a particularly convenient ring of scalars. Indeed, when the scalar ring is the integers, the module is precisely an abelian group. This writeup presents the structure theorem for finitely generated modules over a PID. Although the result is essentially similar to the theorem for finitely generated abelian groups from ea...

متن کامل

MODULES OVER A PID A module over a PID is an abelian group

A module over a PID is an abelian group that also carries multiplication by a particularly convenient ring of scalars. Indeed, when the scalar ring is the integers, the module is precisely an abelian group. This writeup presents the structure theorem for finitely generated modules over a PID. Although the result is essentially similar to the theorem for finitely generated abelian groups from ea...

متن کامل

MODULES OVER A PID A module over a PID is an abelian group

A module over a PID is an abelian group that also carries multiplication by a particularly convenient ring of scalars. Indeed, when the scalar ring is the integers, the module is precisely an abelian group. This writeup presents the structure theorem for finitely generated modules over a PID. Although the result is essentially similar to the theorem for finitely generated abelian groups from ea...

متن کامل

Split Decomposition over an Abelian Group Part 1: Generalities

نویسندگان

چکیده

منابع مشابه

Split decomposition over an abelian group, Part 2: Group-valued split systems with weakly compatible support

Phylogenetic Diversity Over an Abelian Group

MODULES OVER A PID A module over a PID is an abelian group

MODULES OVER A PID A module over a PID is an abelian group

MODULES OVER A PID A module over a PID is an abelian group

ژورنال