Browsing by Author "Teshome, Zelalem (PhD)"

Now showing 1 - 4 of 4
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    Diagonally Singularizable Matrices
    (Addis Ababa University, 2020-06-06) Giovanni, Teumezghi; Teshome, Zelalem (PhD)
    A square matrix A is called diagonally singularizable if / A-S/ < holds for some singular matrix S (I is the identity matrix). The project brings several necessary and/or sufficient conditions for diagonal singularizability and demonstrates another specific feature, namely existence of diagonal singularizability-preserving operations and a theorem of symmetric alternative.
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    Ideal theory of Subtraction Algebras
    (Addis Ababa University, 2008-06-06) Zerihun, Nigatu; Teshome, Zelalem (PhD)
    This project work concentrates on the ideal theory of subtraction algebras. We start it with lattice, semi-lattice, Boolean algebra, supremum and infimum of a set. The main body of the project recapitulates subtraction algebra and ideal of subtraction algebra.
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    Lattice Homomorphism of Lattice Ordered Group
    (Addis Ababa University, 2016-08-01) Ayenew, Zebider; Teshome, Zelalem (PhD)
    In this project, my main concern is to study the Lattice Homomorphism of Lattice Ordered Groups.First we will give the defnition of lattice order group and study its properties. We will see the de_nition given by Stone and Von-Neumann.Next we will defne and study lattice homorphisms. By considering set of all lattice homorphism of a lattice ordered group G. We will show that the homomorphism of G for which (x) = (y) if and only if the set of elements in G disjoint with x is the same as the set disjoint with y, is the maximal lattice homomorphism of G whose kernel is f0g. Finally, we deal with ideal of lattice ordered group and Archimedean Lattice ordered groups
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    On the Theory of Abstract R-Vector Spaces Over a Commutative Regular Ring
    (Addis Ababa University, 2016-01-01) Wondie, Litegebe; Teshome, Zelalem (PhD)
    The notion of an Abstract Boolean Vector space (an Abstract BVector space) is introduced by Subrahmanyam N.V. and he studied intensively on this spaces. Later N.Raja Gopala Rao introduced the concept of an Abstract R-Vector spaces as a generalization of Abstract Boolean Vector space of Subrahmanyam N.V. He introduced the notion of linear endomorphisms and a_ne transformations in Abstract R-Vector spaces and studied its properties. Further, he made a study on the geometric aspect of these spaces. Later K.Venkateswarlu introduced the notion of direct sums in Abstract R-Vector spaces and established that every direct sum of Abstract R-Vector spaces has a basis provided each component has a basis. This thesis is a further continuation on the theory of Abstract RVector spaces. It is investigated by introducing special homomorphisms, strong special homomorphisms, bilinear maps and fractions in Abstract R-Vector Spaces. It is observed that special homomorphism is a normed Abstract R-Vector Space with a suitable norm. Certain properties regarding dual spaces has been obtained like some necessary and su_cient condition for two Abstract R- Vector Spaces to be dual and some interesting results have been proved on fractions in Abstract R-Vector Spaces.