In this paper, we first construct the twisted full toroidal Lie algebra by an extension of a centreless torus LT which is multiloop several automorphisms finite order and equipped with particular grading. We then provide complete classification all irreducible integrable modules finite-dimensional weight spaces for having non-trivial LT-action where centre underlying acts trivially.

It is usually said that two-dimensional (1+1) gauge theories are trivial. In the continuum there are no transverse degrees of freedom to sustain any dynamics. Likewise, in the lattice formulation, the system factorizes (after gauge fixing) and a partition function reduces to a simple one-plaquette integral [1–3]. This picture neglects boundary conditions. It is well known [4] that, e.g., Quantu...

Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading monoid $G$. For each positive integer, the notions of graded-n-coherent module and are introduced. In this paper many results generalized from $n$-coherent rings to graded-$n$-coherent rings. last section, we provide necessary sufficient conditions for trivial extension graded-valuation ri...

Within the field of neuroscience, it is assumed that central nervous system divided into two functionally distinct components: brain, which does cognizing, and spinal cord, a conduit information enabling brain to do its job. We dub this “Cinderella view” cord. Here, we suggest should be abandoned. Marshalling recent empirical findings, claim cord best conceived as an intrabodily cognitive exten...