Decomposition of a Semigroup Structure

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Description

A function to perform the decomposition of a semigroup structure

Usage

1
decomp(S, x, type = c("mc", "pi", "cc"), reduc = FALSE)

Arguments

S

an object of a 'Semigroup' class

x

either an object of a 'Congruence' class or an object of a 'Pi.rels' class

type

whether the reduction is based on a a congruence class or rather on a π-relation or a meet-complement in the 'Pi.rels' class

reduc

(logical) does the return object should include the reduced structures?

Details

The decomp function is a reduction form of an algebraic structure like the semigroup that verifies which of the class members in the system are congruent to each other. The decomposed object then is made of congruent elements, which form part of the lattice of congruence classes in the algebraic structure. In case that the input data comes from the Pacnet program, then such elements are in form of π-relations or the meet-complements of the atoms; otherwise these are simply equivalent elements satisfying the substitution property.

Value

An object of 'Decomp' class having:

clu

vector with the class membership

eq

the equations in the decomposition

IM

(optional) the image matrices

PO

(optional) the partial order table

dims

(optional) a vector with the dimensions of the image matrices

Note

Reduction of the partial order table should be made by the reduc function.

Author(s)

Antonio Rivero Ostoic

References

Pattison, Philippa E. Algebraic Models for Social Networks. Cambridge University Press. 1993.

See Also

cngr, reduc, pi.rels, semigroup, partial.order

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