Diagonal-products and affine completeness

1974 ◽  
Vol 4 (1) ◽  
pp. 269-270
Author(s):  
Heinrich Werner
Keyword(s):  
Affine Completeness

scholarly journals Near-rings of compatible functions

1980 ◽  
Vol 23 (1) ◽  
pp. 87-95 ◽  
Author(s):  
Günter Pilz
Keyword(s):  
Vector Space ◽  
Structure Theory ◽  
Polynomial Functions ◽  
Affine Transformations ◽  
Affine Completeness ◽  
Congruence Relations

SummaryIn this paper we study near-rings of functions on Ω-groups which are compatible with all congruence relations. Polynomial functions, for instance, are of this type. We employ the structure theory for near-rings to get results for the theory of compatible and polynomial functions (affine completeness, etc.). For notations and results concerning near-rings see e.g. (10). However, we review briefly some terminology from there. (N, +,.) is a near-ring if (N, +) is a group and . is associative and right distributive over +. For instance, M(A): = (AA, +, °) is a near-ring for any group (A, +) (° is composition). If N is a near-ring then N0: = {n ∈ N/n0 = 0}. A group (Γ, +) is an N-group (we write NΓ) if a “product” ny is defined with (n + n‛)γ = nγ + n‛γ and (nn‛)γ = n(n‛γ). Ideals of near-rings and N-groups are kernels of (N-) homomorphisms. If Γ is a vector-space, Maff (Γ) is the near-ring of all affine transformations on Γ. N is 2-primitive on NΓ if NΓ is non-trivial, faithful and without proper N-subgroups. The (2-) radical and (2-) semisimplicity are defined similarly to the ring case.

Affine completeness of Kleene algebras

1997 ◽  
Vol 37 (4) ◽  
pp. 477-490 ◽  
Author(s):  
M. Haviar ◽  
K. Kaarli ◽  
M. Plo??ica
Keyword(s):  
Affine Completeness

1-affine completeness of compatible modules

2016 ◽  
Vol 76 (1) ◽  
pp. 99-110 ◽  
Author(s):  
Gary L. Peterson
Keyword(s):  
Affine Completeness

Affine Completeness of Generalised Dihedral Groups

2006 ◽  
Vol 49 (3) ◽  
pp. 347-357 ◽  
Author(s):  
Jürgen Ecker
Keyword(s):  
Direct Product ◽  
Nilpotent Groups ◽  
Necessary Condition ◽  
Dihedral Groups ◽  
Complete Group ◽  
Affine Completeness ◽  
Affine Complete

AbstractIn this paper we study affine completeness of generalised dihedral groups. We give a formula for the number of unary compatible functions on these groups, and we characterise for every k ∈ N the k-affine complete generalised dihedral groups. We find that the direct product of a 1-affine complete group with itself need not be 1-affine complete. Finally, we give an example of a nonabelian solvable affine complete group. For nilpotent groups we find a strong necessary condition for 2-affine completeness.

scholarly journals On affine completeness of distributive p-algebras

1992 ◽  
Vol 34 (3) ◽  
pp. 365-368
Author(s):  
Miroslav Haviar
Keyword(s):  
Boolean Algebra ◽  
Affine Completeness ◽  
Affine Complete

G. Grätzer in [4] proved that any Boolean algebra B is affine complete, i.e. for every n ≥ 1, every function f:Bn→B preserving the congruences of B is algebraic. Various generalizations of this result have been obtained (see [7]–[ll] and [2], [3]).

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