EA-equivalence classes and the more general CCZ-equivalence classes of functions over GF (2) each preserve APN and AB properties desirable for S-box functions. We show that they can be related to subsets c[T ] and g[T ] of equivalence classes [T ] of transversals, respectively, thus clarifying their relationship and providing a new approach to their study. We derive a formula which characterise...

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).

Condition $(PWP)$ which was introduced in (Laan, V., {it Pullbacks and flatness properties of acts I}, Commun. Algebra, 29(2) (2001), 829-850), is related to flatness concept of acts over monoids. Golchin and Mohammadzadeh in ({it On Condition $(PWP_E)$}, Southeast Asian Bull. Math., 33 (2009), 245-256) introduced Condition $(PWP_E)$, such that Condition $(PWP)$ implies it, that is, Condition $...

Newton’s method and its variants are among the most efficient methods known for solving systems of non-linear equations when the functions involved are continuously differentiable. Besides its practical applications, Newton’s method is also a powerful theoretical tool. Therefore, it has been studied and used extensively. One of the famous results on Newton’s method is the well-known Kantorovich...

A monoid S satisfies Condition (A) if every locally cyclic left S-act is cyclic. This condition first arose in Isbell’s work on left perfect monoids, that is, monoids such that every left S-act has a projective cover. Isbell showed that S is left perfect if and only if every cyclic left S-act has a projective cover and Condition (A) holds. Fountain built on Isbell’s work to show that S is left ...

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).