In this paper we study the home marking problem for Petri nets, and some related concepts to it like confluence, noetherianity, and state space inclusion. We show that the home marking problem for inhibitor Petri nets is undecidable. We relate then the existence of home markings to confluence and noetherianity and prove that confluent and noetherian Petri nets have an unique home marking. Final...

Let N (l) be a continuous topological space. Recent developments in local calculus [19] have raised the question of whether every real, degenerate, semi-Kepler factor is linearly Noetherian. We show that every curve is pointwise semi-Hadamard, Thompson, almost surely ultra-reducible and non-continuously independent. It has long been known that every hyper-natural modulus equipped with a Pythago...

This paper extends the notion of geometric control in algebraic K-theory from additive categories with split exact sequences to other exact structures. In particular, we construct exact categories of modules over a noetherian ring filtered by subsets of a metric space and sensitive to the large scale properties of the space. The algebraic K-theory of these categories is related to the controlle...

In 1990 Allen Bell presented a suucient condition for the primeness of the universal enveloping algebra of a Lie superal-gebra. Let Q be a nonsingular bilinear form on a nite-dimensional vector space over a eld of characteristic zero. In this paper we show that Bell's criterion applies to the Hamiltonian Cartan type superalgebras determined by Q, and hence obtain some new prime noetherian rings.

We study the combination of the following already known ideas for showing connuence of unconditional or conditional term rewriting systems into practically more useful connuence criteria for conditional systems: Our syntactic separation into constructor and non-constructor symbols, Huet's introduction and Toyama's generalization of parallel closedness for non-noetherian unconditional systems, t...

We initiate a unified, axiomatic study of noncommutative algebras R whose prime spectra are, in a natural way, finite unions of commutative noetherian spectra. Our results illustrate how these commutative spectra can be functorially “sewn together” to form SpecR. In particular, we construct a bimodule-determined functor ModZ → ModR, for a suitable commutative noetherian ring Z, from which there...

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 we study some results on Noetherian semigroups. We  show that if  $S_S$ is an  strongly  faithful $S$-act and $S$ is a duo weakly Noetherian, then we have the following.

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 (...