‎we present a characterization of arens regular semigroup algebras‎ ‎$ell^1(s)$‎, ‎for a large class of semigroups‎. ‎mainly‎, ‎we show that‎ ‎if the set of idempotents of an inverse semigroup $s$ is finite‎, ‎then $ell^1(s)$ is arens regular if and only if $s$ is finite‎.

In the present paper, we consider biflatness of certain classes of semigroupalgebras. Indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. Also, for a certain class of inversesemigroups S, we show that the biflatness of ell^{1}(S)^{primeprime} is equivalent to the biprojectivity of ell^{1}(S).

in the present paper, we consider biflatness of certain classes of semigroupalgebras. indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. also, for a certain class of inversesemigroups s, we show that the biflatness of ell^{1}(s)^{primeprime} is equivalent to the biprojectivity of ell^{1}(s).

The symmetric quantum Rabi model (QRM) is integrable due to a discrete $\mathbb{Z}_2$-symmetry of the Hamiltonian. This symmetry generated by known involution operator, measuring parity eigenfunctions. An experimentally relevant modification QRM, asymmetric (or biased) (AQRM) no longer invariant under this but shows nevertheless characteristic degeneracies its spectrum for half-integer values $...

Abstract We study the motivic and $$\ell $$ ℓ -adic realizations of dg category singularities zero locus a global section line bundle over regular scheme. will then use formula obtained in this way together with theorem due to D. Orlov J. Burke–M. Walker give for realization vector bundle. In particular, we obt...

Abstract We study the set $${\mathscr {C}}$$ C of mean square values moduli conjugates all nonzero cyclotomic integers $$\beta $$ ? . For its k th derived {C}}^{(k)}$$ ( k ) , we show that {C}}^{(...

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.

We give an algorithm to compute $$(\ell ,\ell )$$ -isogenies from the Jacobians of genus three hyperelliptic curves non-hyperelliptic over a finite field characteristic different 2 in time $$\tilde{O}(\ell ^3)$$ , where $$\ell $$ is odd prime which coprime characteristic. An important application reduce discrete logarithm problem Jacobian curve corresponding curve.