منابع مشابه
Subalgebra Lattices of a Partial Unary Algebra
Necessary and sufficient conditions will be found for quadruples of lattices to be isomorphic to lattices of weak, relative, strong subalgebras and initial segments, respectively, of one partial unary algebra. To this purpose we will start with a characterization of pairs of lattices that are weak and strong subalgebra lattices of one partial unary algebra, respectively. Next, we will describe ...
متن کاملOn Subalgebra Lattices of a Finite Unary Algebra I
One of the main aims of the present and the next part [15] is to show that the theory of graphs (its language and results) can be very useful in algebraic investigations. We characterize, in terms of isomorphisms of some digraphs, all pairs 〈A,L〉, where A is a finite unary algebra and L a finite lattice such that the subalgebra lattice of A is isomorphic to L. Moreover, we find necessary and su...
متن کاملInvestigation of Subalgebra Lattices by Means of Hasse Constants
Hasse constants and their basic properties are introduced to facilitate the connection between the lattice of subalgebras of an algebra C and the natural action of the automorphism group Aut(C) on C. These constants are then used to describe the lattice of subloops of the smallest nonassociative simple Moufang loop.
متن کاملOn Subalgebra Lattices of a Finite Unary Algebra Ii
We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs 〈L1,L2〉 of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to L1 and L2, respectively. Next, we describe other pairs of subalgebra lattices (weak and relative, etc.) of a finite unary algebra. Finally, necessary a...
متن کاملIdeal and Subalgebra Coefficients
For an ideal or K-subalgebra E of K[X1, . . . , Xn], consider subfields k ⊂ K, where E is generated – as ideal or K-subalgebra – by polynomials in k[X1, . . . , Xn]. It is a standard result for ideals that there is a smallest such k. We give an algorithm to find it. We also prove that there is a smallest such k for K-subalgebras. The ideal results use reduced Gröbner bases. For the subalgebra r...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2015
ISSN: 0001-8708
DOI: 10.1016/j.aim.2015.07.027