Article
Mathematics, Applied
Christof Beierle
Summary: This article demonstrates that for every integer d satisfying p < d < 2(p - 1), there exists a generalized almost perfect nonlinear (GAPN) binomial or trinomial over Fp2 with algebraic degree d.
FINITE FIELDS AND THEIR APPLICATIONS
(2023)
Article
Mathematics, Applied
Ahmed Cherchem, Soufyane Bouguebrine, Hamza Boughambouz
Summary: This paper presents two constructions of irreducible polynomials and demonstrates their equivalence. It also offers a characterization of the generator polynomial of BCH codes over F-q and discusses the relationship between two BCH codes over F-q and F-qm with their generator polynomials.
FINITE FIELDS AND THEIR APPLICATIONS
(2022)
Article
Mathematics, Applied
Mohd Arif Raza, Abdul Nadim Khan, Husain Alhazmi
Summary: In this note, we characterize b-generalized derivations which are strong commutative preserving (SCP) on R, and also discuss and characterize b-generalized derivations involving certain *-differential/functional identities on rings possessing involution.
Article
Quantum Science & Technology
Lai-Zhen Luo, Yu Xia, Gui-Jun Zhang
Summary: We study mutually unbiased maximally entangled bases (MUMEBs) in bipartite system C-d⨂C-d with d >= 3, where d is a power of an odd prime number. By utilizing the theory of finite fields, we present a novel and intuitive method for constructing MUMEBs in C-d⨂C-d. Specifically, we construct d(d - 1) MUMEBs in the bipartite system C-d⨂C-d explicitly.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Mathematics
Cheng-Kai Liu
Summary: The conditions described above in a noncommutative prime ring demonstrate that certain restrictions apply to generalized derivations which satisfy specific equations, leading to either linear forms or satisfying particular algebraic structures.
COMMUNICATIONS IN ALGEBRA
(2021)
Article
Mathematics
Ali Ahmed Abdullah, Nazim Khan
Summary: This paper investigates the characterization of weak Jordan right ?-centralizers in prime rings and describes the properties of X-generalized skew derivations which behave like weak Jordan right ?-centralizers.
COMMUNICATIONS IN ALGEBRA
(2023)
Article
Mathematics, Applied
Cheng-Kai Liu
Summary: In this paper, we provide a characterization of the structure of a noncentral Lie ideal L in a prime ring R, as well as the possible forms of two generalized derivations g and h. Based on these results, several known results are either deduced or generalized, including a Lie ideal version of a theorem by Lee and Zhou [An identity with generalized derivations, J. Algebra Appl. 8 (2009) 307-317] and a more complete version of a theorem recently obtained by Dhara and De Filippis [Engel conditions of generalized derivations on left ideals and Lie ideals in prime rings, Comm. Algebra 48 (2020) 154-167].
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Mathematics
Francesco Rania, Vincenzo De Filippis
Summary: This passage discusses a condition regarding prime rings and generalized skew derivations. If a prime ring satisfies a specific equation, then it is either commutative or there exists a certain element q such that the result of the skew derivation is q multiplied by the input element.
COMMUNICATIONS IN ALGEBRA
(2023)
Article
Mathematics
Samuel A. Lopes, Farrokh Razavinia
Summary: This paper introduces and studies a new class of algebras called quantum generalized Heisenberg algebras (qGHA), which encompass a wider range of applications and provide a common framework for several previously studied classes of algebras. The focus is on the classification of finite-dimensional irreducible representations of qGHA, revealing their rich structure. Despite not being generally noetherian, these algebras retain a Lie-theoretic flavor in their representations.
COMMUNICATIONS IN ALGEBRA
(2022)
Article
Mathematics
Mohammad Aslam Siddeeque, Ali Ahmed Abdullah, Nazim Khan
Summary: This paper investigates the properties of generalized derivations K related to the derivation mu in a non-commutative ring R. By proving that K satisfies certain algebraic identities, it is shown that K can only be the identity map, the zero map, or the scalar map. Further discussion is conducted on the case where R embeds in M-2 (C), a matrix ring of order 2x2 over C.
GEORGIAN MATHEMATICAL JOURNAL
(2023)
Article
Mathematics
S. K. Tiwari
Summary: This paper provides a complete characterization of the mappings G, F, and H with respect to the Utumi quotient ring of a prime ring, noncentral multilinear polynomial over the extended centroid, and generalized derivations on the ring.
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
(2022)
Article
Mathematics
Mohammad Aslam Siddeeque, Abbas Hussain Shikeh
Summary: This paper proves, under certain conditions, that if the mappings F and G are additive, then G must equal 0. It also shows that the same conclusion holds under specific conditions, such as when the involution is not the identity map or when A is a PI-ring.
GEORGIAN MATHEMATICAL JOURNAL
(2023)
Article
Mathematics
S. K. Tiwari
Summary: The aim of this paper is to study commuting generalized derivations. We describe all possible forms of T-1, T-2, and T-3 on a prime ring R, where R is a prime ring of char(R) not equal 2, pi(xi(1), ..., xi(n)) is a noncentral multilinear polynomial over C, and T-1, T-2, and T-3 are generalized derivations on R such that T-2(xi)T-1(xi) = T-1(xi)xi - xi T-3(xi) for all xi = pi(xi(1), ..., xi(n)) is an element of f(R).
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
(2023)
Article
Mathematics, Applied
N. Rehman
Summary: This paper examines the properties of a ring R and its relationship with specific equations and subsets, under certain conditions.
ALGEBRA AND DISCRETE MATHEMATICS
(2022)