TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - A characterization of M-solid varieties of semigroups
Y1  - 1999
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Fernandes, Vitor H.
A1  - Koppitz, Jörg
T1  - A note on generators of the endomorphism semigroup of an infinite countable chain
JF  - Journal of Algebra and its Applications
N2  - In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X.
KW  - Infinite chain
KW  - endomorphism semigroup
KW  - generators
KW  - relative rank
Y1  - 2016
U6  - https://doi.org/10.1142/S0219498817500311
SN  - 0219-4988
SN  - 1793-6829
VL  - 16
IS  - 2
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
T1  - All 2-solid varieties of semigroups
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
T1  - All Reg-solid varieties of commutative semigroups
N2  - We determine all regular solid varieties of commutative semigroups. Each of them is contained in the Reg- hyperequational class V (RC) defined by the associative law and the commutative law, and every subvariety of V (RC) is regular solid. In the present paper, the subvariety lattice of V (RC) will be characterized.
Y1  - 2009
UR  - http://www.springerlink.com/content/103374
U6  - https://doi.org/10.1007/s00233-008-9124-y
SN  - 0037-1912
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
A1  - Supaporn, Worakrit
T1  - Categary equivalences of clones of operations preserving unaryoperations
JF  - COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
N2  - Any clones on arbitrary set A can be written of the form Pol (A)Q for some set Q of relations on A. We consider clones of the form Pal (A)Q where Q is a set of unary relations on a finite set A. A clone Pol (A)Q is said to be a clone on a set of the smallest cardinality with respect to category equivalence if vertical bar A vertical bar <= vertical bar S vertical bar for all finite sets S and all clones C on S that category equivalent to Pol (A)Q. We characterize the clones on a set of the smallest cardinality with respect to category equivalent and show how we can find a clone on a set of the smallest cardinality that category equivalent to a given clone.
KW  - category equivalence of clones
KW  - clone of operations
Y1  - 2013
SN  - 1310-1331
VL  - 66
IS  - 2
SP  - 177
EP  - 184
PB  - Publ. House of the Bulgarian Acad. of Sciences
CY  - Sofia
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
A1  - Marszalek, R.
T1  - Derived varieties and derived equational theories
Y1  - 1998
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
A1  - Niwczyk, St.
T1  - Equational theories generated by generalized hypersubstitutions of type (n)
Y1  - 2002
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Essential variables in hypersubstitution
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Essential variables in weak hypersubstitutions
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Finite monoids of hypersubstitutions of type € = (2)
Y1  - 1998
ER  -