We prove that the m-generated Grassmann algebra can be embedded into a 2 × 2 matrix algebra over a factor of a commutative polynomial algebra in m indeterminates. Cayley–Hamilton and standard identities for n× n matrices over the m-generated Grassmann algebra are derived from this embedding. Other related embedding results are also presented.

The aim of this article is to study the concept of unique solvability of max-min fuzzy neutrosophic soft matrix equation and strong regularity of fuzzy neutrosophic soft matrices over Fuzzy Neutrosophic Soft Algebra (FNSA). A Fuzzy Neutrosophic Soft Matrix (FNSM) is said to have Strong, Linear Independent (SLI) column (or, in the case of fuzzy neutrosophic soft square matrices, to be strongly r...

Connections between set-theoretic Yang-Baxter and reflection equations quantum integrable systems are investigated. We show that $R$-matrices expressed as twists of known solutions. then focus on twisted algebras we derive the associated defining algebra relations for being Baxterized solutions $A$-type Hecke ${\cal H}_N(q=1)$. in case there exists a ``boundary'' finite sub-algebra some special...

We find a new braided Hopf structure for the algebra satisfied by the entries of the braided matrix BSLq(2). A new nonbraided algebra whose coalgebra structure is the same as the braided one is found to be a two parameter deformed algebra. It is found that this algebra is not a comodule algebra under adjoint coaction. However, it is shown that for a certain value of one of the deformation param...