One dimensional Witt's theorem over modular lattices
نویسندگان
چکیده
منابع مشابه
One Dimensional Topological Lattices
The lattice theoretic terminology used in this paper is consistent with Birkhoff [2]. The topological terms can be found in [5] or [8] with the following exceptions. If X and Y are sets, X\Y denotes the relative compliment of Y with respect to X. If A is a subset of a topological space then A*, A"and FiA)=A*\A° denote the topological closure, interior and boundary of A. The symbol 0 denotes the...
متن کاملThe Hyperradical and the Hopkins–levitzki Theorem for Modular Lattices
Many arguments in the Theory of Rings and Modules are, on close inspection, purely Lattice theoretic arguments. Cǎlagǎreanu has a long repertoire of such results in his book. The Hopkins-Levitzki Theorem is interesting from this point of view, because a special case of it lends to an obvious lattice theory approach, but the rest is a little more subtle. Albu and Smith have obtained some suffici...
متن کاملThe Jónsson Theorem about the Representation of Modular Lattices
Let A be a non empty set and let P , R be binary relations on A. Let us observe that P ⊆ R if and only if: (Def. 1) For all elements a, b of A such that 〈a, b〉 ∈ P holds 〈a, b〉 ∈ R. Let L be a relational structure. We say that L is finitely typed if and only if the condition (Def. 2) is satisfied. (Def. 2) There exists a non empty set A such that (i) for every set e such that e ∈ the carrier of...
متن کاملUnsolvable One-dimensional Lifting Problems for Congruence Lattices of Lattices
Let S be a distributive {∨, 0 }-semilattice. In a previous paper, the second author proved the following result: Suppose that S is a lattice. Let K be a lattice, let φ : Conc K → S be a {∨, 0 }-homomorphism. Then φ is, up to isomorphism, of the form Conc f , for a lattice L and a lattice homomorphism f : K → L. In the statement above, Conc K denotes as usual the {∨, 0 }-semilattice of all finit...
متن کاملInterparticle gap distributions on one-dimensional lattices
We analyse the successive binding of two species of particles on a onedimensional discrete lattice, where the second variety is deposited only after complete adsorption of the first. We consider the two extreme cases of a perfectly irreversible initial deposition, with non-sliding particles, and that of a fully equilibrated one. For the latter we construct the exact gap distribution from the To...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1970
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1970-12388-6