1. The core of a vertex-transitive complementary prismMarko Orel, 2023, original scientific article Abstract: The complementary prism ▫$\Gamma \overline{\Gamma}$▫ is obtained from the union of a graph ▫$\Gamma$▫ and its complement ▫$\overline{\Gamma}$▫ where each pair of identical vertices in ▫$\Gamma$▫ and ▫$\overline{\Gamma}$▫ is joined by an edge. It generalizes the Petersen graph, which is the complementary prism of the pentagon. The core of a vertex-transitive complementary prism is studied. In particular, it is shown that a vertex-transitive complementary prism ▫$\Gamma \overline{\Gamma}$▫ is a core, i.e. all its endomorphisms are automorphisms, whenever ▫$\Gamma$▫ is a core or its core is a complete graph.
Keywords: graph homomorphism, complementary prism, self-complementary graph, vertex-transitive graph, core
Published in RUP: 06.11.2023; Views: 782; Downloads: 5
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3. Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)Marko Orel, Bojan Kuzma, 2009, original scientific article Abstract: A complete classification of additive rank-one nonincreasing maps on hermitian matrices over Galois field ▫$GF(2^2)$▫ is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rank-additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented.
Keywords: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph
Published in RUP: 03.04.2017; Views: 2541; Downloads: 87
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4. Jordan [tau]-derivations of locally matrix ringsChen-Lian Chuang, Ajda Fošner, Tsiu Kwen Lee, 2013, original scientific article Abstract: Let ▫$R$▫ be a prime, locally matrix ring of characteristic not 2 and let ▫$Q_{ms}(R)$▫ be the maximal symmetric ring of quotients of ▫$R$▫. Suppose that ▫$\delta \colon R \to Q_{ms}(R)$▫ is a Jordan ▫$\tau$▫-derivation, where ▫$\tau$▫ is an anti-automorphism of $R$. Then there exists ▫$a \in Q_{ms}(R)$▫ such that ▫$\delta(x) = xa - a\tau(x)$▫ for all ▫$x \in R$▫. Let ▫$X$▫ be a Banach space over the field ▫$\mathbb{F}$▫ of real or complex numbers and let ▫$\mathcal{B}(X)$▫ be the algebra of all bounded linear operators on ▫$X$▫. We prove that ▫$Q_{ms}(\mathcal{B}(X)) = \mathcal{B}(X)$▫, which provides the viewpoint of ring theory for some results concerning derivations on the algebra ▫$\mathcal{B}(X)$▫. In particular, all Jordan ▫$\tau$▫-derivations of ▫$\mathcal{B}(X)$▫ are inner if ▫$\dim_{\mathbb{F}} X>1$▫.
Keywords: mathematics, algebra, anti-automorphism, locally matrix ring, prime ring, Jordan homomorphism, Jordan ▫$\tau$▫-derivation, Banach space
Published in RUP: 15.10.2013; Views: 3830; Downloads: 83
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