We propose a concept of module liaison that extends Gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative Gorenstein ring. Analyzing the resulting equivalence classes we show that several results known for Gorenstein liaison are still true in the more general case of module liaison. In particular, we construct two maps from the set of even li...

The paper describes the set of solutions of the discrete-time algebraic Riccati equation. It is shown that each solution is a combination of a pair of opposite unmixed solutions. There is a one-to-one correspondence between solutions and invariant subspaces of the closed loop matrix of an unmixed solution. The results of the paper provide an extended counterpart of the parametrization theory of...

We carry out general relativistic ray-tracing radiative-transfer calculations to study whether a localized emission from $e^{\pm}$ plasma rings created at the stagnation surface in jet funnel, which we refer as rings, can explain ring image of M87 observed by Event Horizon Telescope (EHT) 2017. The resultant images consist direct and formed via strong deflection black-hole (BH) gravity, "quasi ...

We introduce the Singleton bounds for codes over a finite commutative quasi-Frobenius ring.

This paper presents an outline of the handling and recycling of SF6 mixtures in electrical power equipment. It is based on the CIGRE Guide for SF6 mixtures and addresses the application fields of SF6 mixtures in electric power equipment, their insulation and switching performance, the evaluation of their environmental advantage, and the processes and equipment for their environmentally responsi...

Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...

In this paper we investigate how algorithms for computing heights, radicals, unmixed and primary decompositions of ideals can be lifted from a Noetherian commutative ring R to polynomial rings over R. It is a standard problem in mathematics to study which properties of a mathematical structure are preserved in derived structures. A typical result of this kind is the Hilbert Basis Theorem which ...