The concept of multipliers in an Almost Semilattice(ASL) is introduced and some basic properties are proved. More over, in an ASL L, we introduced a congruence relation $\phi_{a}$ for $a\in L$ and some useful properties of $\phi_{a}$ are derived.

 By definition primitive and $2$-primitive elements of a finite field extension $\Fn$ have order $q^n-1$ and $(q^n-1)/2$, respectively. We have already shown that, with minor reservations, there exists a primitive element and a $2$-primitive element $\xi \in \Fn$ with prescribed trace in the ground field $\F_q$. Here we amend our previous proofs of these results, firstly, by a reduction of these problems to extensions of prime degree $n$ and, secondly, by deriving an exact expression for the number of squares in $\Fn$ whose trace has prescribed value in $\F_q$. The latter corrects an error in the proof in the case of $2$-primitive elements. We also streamline the necesary computations.

 The notion of factor set in Lie algebras is defined by Moneyhun in $1994$. It was developed by Eshrati et al. on $n$-Lie algebras. In this paper we present an $m$-factor set notion on Filippov algebras and obtain some results for finite dimensional $m$-stem Filippov algebras. Moreover, we show that if $A$ and $B$ are two finite dimensional $m$-stem Filippov algebras or have the same dimensions, then $A\sim_m B$ if and only if $A\cong B$.

 In this paper, we proved that each nonlinear non-global semi-Jordan triple higher derivable mapping on a $2$-torsion free triangular algebra is an additive higher derivation. As its application, we get the similar conclusion on a nest algebra or a $2$-torsion free block upper triangular matrix algebra, respectively.

 In this paper, the notion of soft normal int-field over a field has been introduced. We have established a correspondence, called Soft Galois correspondence, between the soft intermediate int-fields of a finite Galois extension and the soft int-groups of the Galois group corresponding to the field extension. We have generalized some results of Galois theory in the environment of soft set theory.

 This paper is an attempt to study ordered semigroups which are nil-exten\-sions of simple and $\pi$-inverse ordered semigroups. Different characterizations of complete semilattice decomposition of nil-extensions of ordered semigroups have been given here.

 We prove several norm and numerical radius inequalities for linear operators in Hilbert spaces. In particular, it is proved that if $A$ is a bounded linear operator on a complex Hilbert space, then

 We introduce $L^r$-Henstock-Kurzweil integral for finite dimensional Banach spaces. We discuss its properties. In this study we discuss $L^r$-Henstock-Kurzweil integral generalized Henstock-Kurzweil integral for finite dimensional Banach spaces.

 Let $KG$ be the group algebra of a group $G$ over a field $K$ of characteristic $p>0$. The classification of group algebras $KG$ with upper Lie nilpotency index $t^{L}(KG)$ up to 14 has already been done. In this paper, we classify the group algebras $KG$ having upper Lie nilpotency index 15, for $G'= \gamma_{2}(G)$ as an abelian group.

 The notion of an action $ \sigma $ of a locale $ L $ on a join semilattice $ J $ with bottom element $ 0_{J} $ is developed and utilized to form the entity $ (\sigma,J) $, which we call L-slice, has properties that could be studied algebraically as well as topologically. In this study, the existence of a contravariant functor from a subcategory of the category $L$-slice, of L-slices and L-slice homomorphisms, into the category TopWMod, of topological weak modules and continuous weak module homomorphisms, has been established.

 An act $A_S$ satisfies Condition $(PWP)$ if $as=a^\prime s$ for $a, a^\prime \in A_S, s\in S$ implies that there exist $a ^{\prime\prime} \in A_S$ and $ u, v\in S $ such that $ a=a^{\prime\prime} u$, $a^\prime = a^{\prime\prime} v$ and $us=vs$. In this paper we introduce a generalization of Condition $(PWP)$ called Condition $(L_{PWP})$ and will characterize monoids using this property. It can be seen easily that any right locally cyclic act satisfies Condition ($L_{PWP}$).