In recent work we called a ring R a GGCD ring if the semigroup of finitely generated faithful multiplication ideals of R is closed under intersection. In this paper we introduce the concept of generalized GCD modules. An R-moduleM is a GGCD module if M is multiplication and the set of finitely generated faithful multiplication submodules of M is closed under intersection. We show that a ring R ...

Let E ∼= (Z/p)r (r ≥ 2) be an elementary abelian p-group and let k be an algebraically closed field of characteristic p. A finite dimensional kE-module M is said to have constant Jordan type if the restriction of M to every cyclic shifted subgroup of kE has the same Jordan canonical form. I shall begin by discussing theorems and conjectures which restrict the possible Jordan canonical form. The...

In computer science, there is a distinction between closed systems, whose behavior is totally determined in advance, and open systems, that are systems maintaining a constant interaction with an unspecified environment. Closed systems are naturally modeled by transitions systems. Open systems have been modeled in various ways, including process algebras, I/O automata, “modules”, and interfaces....

The formatted protein sequence space is built from identical size fragments of prokaryotic proteins (112 complete proteomes). Connecting sequence-wise similar fragments (points in the space) results in the formation of numerous networks, that combine sometimes different types of proteins sharing, though, fragments with similar or distantly related sequences. The networks are mapped on individua...

We propose a discrete nonlinear controller, developed in a synchronous frame, for a parallel three-phase boost converter consisting of two modules. The basic idea, however, can be extended to a system with modules. Each of the closed-loop power-converter modules operates asynchronously without any communication with the other modules. The controller stabilizes the currents on the -axes and limi...

Let $G$ be an abelian group with identity $e$. $R$ a $G$-graded commutative ring identity, $M$ graded $R$-module and $S\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, we introduce the concept $S$-prime submodules modules over rings. We investigate some properties class their homogeneous components. $N$ submodule such that $(N:_{R}M)\cap S=\emptyset $. say is \textit{a }$S$...

Let A = L i≥0 Ai be a connected graded, noetherian k-algebra that is generated in degree one over an algebraically closed field k. Suppose that the graded quotient ring Q(A) has the form Q(A) = k(X)[t, t, σ], where σ is an automorphism of the integral projective surface X. Then we prove that A can be written as a näıve blowup algebra of a projective surface X birational to X. This enables one t...

A rational Mackey functor M for a compact Lie group G can be viewed as a collection of sheaves on spaces of conjugacy classes of subgroups, one for each closed subgroup H, related by restriction maps only. This in turn may be speciied by giving a suitably continuous family consisting of a Q 0 (W G (H))-module V (H) for each closed subgroup H with restriction maps V (^ K) ?! V (K) whenever K is ...