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1
Title: Multipliers in Almost Semilattices
Vol.48(2) (2024) page: 151-159
Author(s): T.G. Beyene and H.T. Alemu
Abstract: 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.
Keywords: Semilattices; Almost semilattice; Almost semilattice with zero; Multiplier; Isoton; Idempotent; $Fix_{f}(L)$. |
2
Title: The Trace of Primitive and $2$-Primitive Elements, Revisited
Vol.48(2) (2024) page: 161-184
Author(s): S.D. Cohen and G. Kapetanakis
Abstract: 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.
Keywords: Primitive elements; Trace function. |
3
Title: Some Properties of $m$-factor Set on Filippov Algebras
Vol.48(2) (2024) page: 185-194
Author(s): A. Doosti
Abstract: 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 $A\cong B$.
Keywords: Lie algebra; Isoclinic; $m$-Isoclinism; $n$-Lie algebras. |
4
Title: A Class of Nonlinear Non-global Semi-Jordan Triple Higher Derivable Mappings on Triangular Algebras
Vol.48(2) (2024) page: 195-210
Author(s): X.H. Fei and G.W. Zhu
Abstract: 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.
Keywords: Semi-Jordan triple derivable mapping; Semi-Jordan triple higher derivable mapping; Derivation; Higher derivation. |
5
Title: Galois Theory for Soft Int-field
Vol.48(2) (2024) page: 211-226
Author(s): J. Ghosh, D. Mandalz and T.K. Samanta
Abstract: 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.
Keywords: Soft set; Soft int-field; Soft normal int-field; Soft Galois correspondence. |
6
Title: Nil-Extensions of Simple and $\pi$-Inverse Ordered Semigroups
Vol.48(2) (2024) page: 227-235
Author(s): K. Hansda and A. Jamadarg
Abstract: 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.
Keywords: $l$-Archimedean; $\pi$-Regular; Nil-Extension; Ordered idempotent; Simple ordered semigroup; $\pi$-Inverse ordered semigroup. |
7
Title: Upper Bounds for the Numerical Radius of Hilbert Space Operators
Vol.48(2) (2024) page: 237-245
Author(s): E. Jaafari, M.S. Asgari, M.S. Hosseini and B. Moosavi
Abstract: 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
\[{{\omega }^{2}}\left( A \right)\le \frac{1}{2}\left( \omega \left( \left| {{A}^{*}} \right|\left| A \right| \right)+{{\left\| A \right\|}^{2}} \right),\]
where $\omega \left( A \right)$, $\left\| A \right\|$, and $\left| A \right|$ are the numerical radius, the usual operator norm, and the absolute value of $A$, respectively.
Keywords: Numerical radius; Operator norm; Convex function; Positive operator. |
8
Title: $L^r$-Henstock-Kurzweil Integral on Finite Dimensional Banach Spaces
Vol.48(2) (2024) page: 247-258
Author(s): H. Kalita, T.P. Becerra and H. Bharali
Abstract: 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.
Keywords: $L^r$-Henstock-Kurzweil integral; Banach valued $L^r$-Henstock-Kurzweil integral. |
9
Title: Group Algebras of Lie Nilpotency Index 15
Vol.48(2) (2024) page: 259-271
Author(s): A. Mishra, H. Chandra and S. Bhatt
Abstract: 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.
Keywords: Group algebras; Lie nilpotency index; Lie dimension subgroup. |
10
Title: Category $L$-Slice and its Properties
Vol.48(2) (2024) page: 273-284
Author(s): K.S. Sabna and N.R. Mangalambal
Abstract: 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.
Keywords: Weak $L$-module; Weak $L$-module homomorphism; Weak $L$-submodule and topological weak modules. |
11
Title: Generalization of Condition $(PWP)$
Vol.48(2) (2024) page: 285-296
Author(s): M.R. Zamani, H. Mohammadzadeh Saany and P. Rezaei
Abstract: 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 ($L_{PWP}$).
Keywords: $S$-act; Condition $(PWP)$; Locally cyclic; Condition $(P)$. |
11 Records!
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