We show that T (F)= = E can be completely axiomatized when = E is a quasi-free theory. Quasi-free theories are a wider class of theories than permutative theories of Mal71] for which Mal'cev gave decision results. As an example of application, we show that the rst order theory of T (F)= = E is decidable when E is a set of ground equations. Besides, we prove that the 1-fragment of the theory of ...

The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The Markov triplet is defined by constant entropy increase. The Markov property of a quasi-free state is described by the representing block matrix. The proof is based on results on the statistical sufficien...

A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characte...

In this paper, we study equivalences between the categories of quasi-coherent sheaves on non-commutative noetherian schemes. particular, give a new proof Caldararu's conjecture about Morita Azumaya algebras Moreover, derive necessary and sufficient condition for two reduced curves to be equivalent.

A ring $R$ with an automorphism $sigma$ and a $sigma$-derivation $delta$ is called $delta$-quasi-Baer (resp., $sigma$-invariant quasi-Baer) if the right annihilator of every $delta$-ideal (resp., $sigma$-invariant ideal) of $R$ is generated by an idempotent, as a right ideal. In this paper, we study Baer and quasi-Baer properties of skew PBW extensions. More exactly, let $A=sigma(R)leftlangle x...

We introduce a coloured generalization $\mathrm{NSym}_A$ of the Hopf algebra non-commutative symmetric functions described as subalgebra rooted ordered trees algebra. Its natural basis can be identified with set sentences over alphabet $A$ (the colours). present also its graded dual $\mathrm{QSym}_A$ quasi-symmetric together realization in terms power series partially commutative variables. pro...

We discuss the converse of a theorem of Potter stating that if the matrix equation AB = ωBA is satisfied with ω a primitive qth root of unity, then Aq+Bq = (A+B)q. We show that both conditions have to be modified to get a converse statement and we present a characterization when the converse holds for these modified conditions and q = 3 and a conjecture for the general case. We also present som...

In Hanaki (Graphs Combin 37:1521–1529, 2021), defined the Terwilliger algebras of association schemes over a commutative unital ring. this paper, we call field $${\mathbb {F}}$$ -algebras and study quasi-thin schemes. As main results, determine -dimensions, semisimplicity, Jacobson radicals, algebraic structures