Bruck decomposition for endomorphisms of quasigroups

An holomorphic study of Smarandache automorphic and cross inverse property loops

By studying the holomorphic structure of automorphic inverse property quasigroups and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache; AIPL, CIPL, Kloop, Bruck-loop or Kikkawa-loop if and only if its Smarandache automorphism group is trivial and the loop is itself is a Smarandache; AIPL, CI...

Right Product Quasigroups and Loops

Right groups are direct products of right zero semigroups and groups and they play a significant role in the semilattice decomposition theory of semigroups. Right groups can be characterized as associative right quasigroups (magmas in which left translations are bijective). If we do not assume associativity we get right quasigroups which are not necessarily representable as direct products of r...

Decomposition of Additive CA

We consider finite additive cellular automata with fixed and periodic boundary conditions as endomorphisms over pattern spaces. A characterization of the nilpotent and regular parts of these endomorphisms is given in terms of their minimal polynomials. We determine the generalized eigenspace decomposition, and describe relevant cyclic subspaces in terms of symmetries. As an application, we calc...

Decomposition of Additive Cellular Automata

Finite additive cellular automata with fixed and periodic boundary conditions are considered as endomorphisms over pattern spaces. A characterization of the nilpotent and regular parts of these endomorphisms is given in terms of their minimal polynomials. Generalized eigenspace decomposition is determined and relevant cyclic subspaces are described in terms of symmetries. As an application, the...

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra