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On the concepts of torsion and divisibility for general ringsWei, Diana Yun-Dee. January 1967 (has links)
No description available.
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Purity and flatnessFieldhouse, David J. January 1967 (has links)
No description available.
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On near rings associated with free groupsZeamer, Richard Warwick. January 1977 (has links)
No description available.
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Topological f-rings.Armstrong, Kenneth William January 1965 (has links)
No description available.
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Near-rings and their modulesBerger, Amelie Julie 18 July 2016 (has links)
A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand, Johannesburg, 1991. / After an introduction defining basic structutral aspects of near-rings, this report examines how the ring-theoretic notions of generation and cogeneration can be
extended from modules over a ring to modules over a near-ring. Chapter four examines matrix near-rings and connections between the J2 and JS radicals of the near-ring and the corresponding matrix near-ring.
By extending the concepts of generation and cogeneration from the ring modules
to near-ring modules we are investigating how important distribution and an abelian
additive structure are to these two concepts. The concept of generation faces the
obstacle that the image of a near-ring module homomorphism is not necessarily a
subrnodule of the image space but only a subgroup, while the sum of two subgroups need not even be a subgroup. In chapter two, generation trace and socle are defined for near-ring modules and these ideas are linked with those of the essential
and module-essential subgroups. Cogeneration, dealing with kernels which are always
submodules proved easier to generalise. This is discussed in chapter three
together with the concept of the reject, and these ideas are Iinked to the J1/2
and J2 radicals. The duality of the ring theory case is lost. The results are less
simple than in the ring theory case due to the different types of near-ring module
substructures which give rise to several Jacobson-type radicals.
A near-ring of matrices can be obtained from an arbitrary near-ring by
regarding each rxr matrix as a mapping from Nr to Nr where N is the near-ring
from which entries are taken. The argument showing that the near-ring is
2-semisimple if and only if the associated near-ring of matrices is 2-semisimple
is presented and investigated in the case of s-semisimplicity.
Questions arising from this report are presented in the final chapter.
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Torsion theories, ring extensions, and group ringsLouden, Kenneth C. January 1975 (has links)
No description available.
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A knapsack-type cryptographic system using algebraic number ringsMoyer, Nathan Thomas. January 2010 (has links) (PDF)
Thesis (Ph. D.)--Washington State University, May 2010. / Title from PDF title page (viewed on May 21, 2010). "Department of Mathematics." Includes bibliographical references (p. 83-86).
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Normed ringsUnknown Date (has links)
"A topological ring can be defined as a Hausdorff space which is a ring whose operations are continuous in both variables simultaneously. The purpose of this paper is to present a development of a branch of topological rings, normed rings. Chapter I presents the algebraic concepts and Chapter II, the topological concepts which are basic to the understanding of the remaining chapters. Chapter III is devoted to theory of Banach spaces and linear transformations. Chapter IV gives a treatment of normed rings, particularly the rings of continuous functions of a compact topological space. The latter part of this chapter presents a characterization of these rings"--Introduction. / Typescript. / "August, 1955." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Advisor: M. J. Walsh, Professor Directing Paper. / Includes bibliographical references (leaf 51).
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Torsion theories, ring extensions, and group ringsLouden, Kenneth C. January 1975 (has links)
No description available.
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THE ISOMORPHISM PROBLEM FOR COMMUTATIVE GROUP ALGEBRAS.ULLERY, WILLIAM DAVIS. January 1983 (has links)
Let R be a commutative ring with identity and let G and H be abelian groups with the group algebras RG and RH isomorphic as R-algebras. In this dissertation we investigate the relationships between G and H. Let inv(R) denote the set of rational prime numbers that are units in R and let G(R) (respectively, H(R)) be the direct sum of the p-components of G (respectively, H) with p ∈ inv(R). It is known that if G(R) or H(R) is nontrivial then it is not necessarily true that G and H are isomorphic. However, if R is an integral domain of characteristic 0 or a finitely generated indecomposable ring of characteristic 0 then G/G(R) ≅ H/H(R). This leads us to make the following definition: We say that R satisfies the Isomorphism Theorem if whenever RG ≅ RH as R-algebras for abelian groups G and H then G/G(R) ≅ H/H(R). Thus integral domains of characteristic 0 and finitely generated indecomposable rings of characteristic 0 satisfy the Isomorphism Theorem. Our first major result shows that indecomposable rings of characteristic 0 (no restrictions on generation) satisfy the Isomorphism theorem. It has been conjectured that all rings R satisfy the Isomorphism Theorem. However, we show that the conjecture may fail if nontrivial idempotents are present in R. This leads us to consider necessary and sufficient conditions for rings to satisfy the Isomorphism Theorem. We say that R is an ND-ring if whenever R is written as a finite product of rings then one of the factors, say Rᵢ, satisfies inv(Rᵢ) = inv(R). We show that every ring satisfying the Isomorphism Theorem is an ND-ring. Moreover, if R is an ND-ring and if inv(R) is not the complement of a single prime we show that R must satisfy the Isomorphism Theorem. This result together with some other fragmentary evidence leads us to conjecture that R satisfies the Isomorphism Theorem if and only if R is an ND-ring. Finally we obtain several equivalent formulations of our conjecture. Among them is the result that every ND-ring satisfies the Isomorphism Theorem if and only if every field of prime characteristic satisfies the Isomorphism Theorem.
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