We obtain a complete structural characterization of Cohn-Leavitt algebras over no-exit objects as graded involutive algebras. Corollaries of this result include graph-theoretic conditions characterizing when a Leavitt path algebra is a directed union of (graded) matricial algebras over the underlying field and over the algebra of Laurent polynomials and when the monoid of isomorphism classes of...

Let us mention that every non empty relational structure which is trivial and reflexive is also complete. Let T be a relational structure. A type of T is an element of T . Let T be a relational structure. We say that T is Noetherian if and only if: (Def. 1) The internal relation of T is reversely well founded. Let us observe that every non empty relational structure which is trivial is also Noe...

In this paper, for noetherian commutative ring with a unit A such that every finitely generated A-module is free, and for a certain A-regular sequence f1, · · · , fp, we define Kos(A; f1, · · · , fp) the category of Koszul cubes associated to f1, · · · , fp which has a natural Waldhausen categorical structure. We also give a new algorithm of resolution process of modules by Koszul cubes. By the...

Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids (semigroups). Noetherian ordered groupoids (...

Copyright q 2012 Derya Keskin T ¨ utüncü et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. It is proved that if L is a complete modular lattice which is compactly generated, then RadL/0 is Artinian if, and only if for every s...

Let i : A → R be a ring morphism, and χ : R → A a right R-linear map with χ(χ(r)s) = χ(rs) and χ(1 R) = 1 A. If R is a Frobenius A-ring, then we can define a trace map tr : A → A R. If there exists an element of trace 1 in A, then A is right FBN if and only if A R is right FBN and A is right noetherian. The result can be generalized to the case where R is an I-Frobenius A-ring. We recover resul...

Given a valuation on the function field k(x, y), we examine the set of images of nonzero elements of the underlying polynomial ring k[x, y] under this valuation. For an arbitrary field k, a Noetherian power series is a map z : Q → k that has Noetherian (i.e., reverse well-ordered) support. Each Noetherian power series induces a natural valuation on k(x, y). Although the value groups correspondi...

We study some cardinal invariants of an order-theoretic fashion on products and box products of topological spaces. In particular, we concentrate on the Noetherian type (Nt), defined by Peregudov in the 1990s. Some highlights of our results include: (1) There are spaces X and Y such that Nt(X×Y ) < min{Nt(X), Nt(Y )}. (2) In several classes of compact spaces, the Noetherian type is preserved by...

Let I (α) ≤ a. It was Taylor–Cavalieri who first asked whether hulls can be computed. We show that |s|−3 = 0−1. Is it possible to construct hulls? U. Newton [11] improved upon the results of V. Wang by extending hyper-nonnegative domains.