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Porings and poring algebras

Jun Y., Kim H., Neggers J.

Demonstratio Mathematica

2006

Vol. 39, nr 2

267-276

In this paper we define an algebra of type (2,2,0) associated with posets called a poring and we study several properties of porings and the linear algebras having such porings as their bases. In particular, we show that if (P; *, .) is a standard poring then the distributive law (x . y) * z = (x * z) . (y * z) holds iff the poset P (or the poset X) is (C2 +1)-free.

Algebras associated with posets

Neggers J., Kim H. S.

Demonstratio Mathematica

2001

Vol. 34, nr 1

13-23

In this paper we introduce a class of algebras whose bases over a field K are pogroupoids. We discuss several properties of these algebras as they relate to the structure of their associated pogroupoids and through these to the associated posets also. In particular the Jacobi form is O precisely when the pogroupoid is a semigroup, precisely when the posets is (C2 + 1)-free. Thus, it also follows that a pg-algebra KS over a field K is a Lie algebra with respect to the commutator product iff its associated posets S(<) is (C2 +1)-free. The ideals generated by commutators have some easily identifiable properties m terms of the incomparability graph of the posets associated with the pogroupoid base of the algebra. We conjecture that a fundamental theorem on the relationship between isomorphic algebras and isomorphic pogroupoids holds as well.