Pursuit and evasion on a ring: An infinite hierarchy for parallel real—time systems

In this work, we propose a new quantum structure--weak quantum MV algebras (wQMV algebras)--and define coupled bimonoids and strong coupled bimonoids. We find that the coupled bimonoids and strong coupled bimonoids are ring-like structures corresponding ...

In 1988, given a complete Brouwerian lattice $\mathbb{L}:=(L;\wedge ,\vee ;0,1)$ and a ring $\mathcal{A}:=(A;+,·;-;0)$ with unity 1, Swamy and Swamy (J Math Anal Appl 134:94–103, 1988) built a lattice structure, on the set of L-fuzzy ideals of $\mathcal{A}$, and investigated some of its ...$\mathcal{}\mathrm{}\mathrm{}$$\mathcal{}\mathcal{}\mathcal{}{}_{\mathrm{}}\underset{}{\mathrm{}}$$\mathcal{}$$\mathcal{}$$\mathcal{}$$\mathcal{}\mathcal{}\mathcal{}\mathrm{}$$\mathcal{}$$\mathcal{}$

Schur’s Lemma says that the endomorphism ring of a simple left R-module is a division ring. It plays a fundamental role to prove classical ring structure theorems like the Jacobson Density Theorem and the Wedderburn–Artin Theorem. We first define ...${\mathrm{}}_{\mathrm{}}^{\mathrm{}}$$\mathrm{}{}_{\mathrm{}}$${}_{}$