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Document Type |
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Thesis |
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Document Title |
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PRIME AND SEMIPRIME RINGS ADMITTING DERIVATIONS AND OTHER KINDS OF MAPPINGS الحلقات الأولية و شبه الأولية التي تقبل الإشتقاقيات و أنواع أُخرى من الرواسم |
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Subject |
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Girls' College of Education in Jeddah |
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Document Language |
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Arabic |
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Abstract |
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In this dissertation, all our studies concern rings admitting some types of derivations and other kinds of mappings. We divide it into nine chapters. All our new results are included in chapters 2 - 9.
Chapter One. This introductory chapter contains some basic concepts and results concerning prime rings, semiprime rings, Martindale rings of quotients, and maximal right quotient rings. Also, it contains the previous results in the literature concerning different kinds of derivations.
Chapter Two. We prove that some algebraic conditions are equivalent to commutativity of prime rings admitting nonzero derivations on left ideals. Then we study some algebraic conditions which imply the commutativiy of prime rings.
Chapter Three. We prove that some algebraic conditions lead semiprime rings admitting derivations to possess nonzero central ideals. Also we study nonzero ideals which are central.
Chapter Four. We study prime rings admitting derivations which satisfy some algebraic conditions on Lie ideals. Then we
study strong commutativity preserving derivations on Lie ideals.
Chapter Five. We study the condition d(xm+n+1) + xmd(x)xnZ(R) on a prime ring with certain restrictions characteristic, where d is a nonzero derivation, that lead the ring to be commutative.
Chapter Six. We study the influence of a map of period two on a ring when this map is a derivation, an - derivation, and a generalized derivation.
Chapter Seven. We show that a multiplicative centralizer on a prime ring containing an idempotent element e 0, 1 is additive.
Chapter Eight. We study generalized derivations and generalized (, )- derivations in prime and semiprime rings. We introduce the concept of a generalized left derivation, and we prove that every generalized left derivation on a semiprime ring is a generalized derivation. Also study the orthogonality of generalized (, )- derivations and get some results.
Chapter Nine. We study dependent elements on some
mappings. We introduce the concept of two dependent elements and study this concept on prime and semiprime rings. |
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Supervisor |
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dr. |
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Thesis Type |
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Doctorate Thesis |
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Publishing Year |
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1430 AH
2009 AD |
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Added Date |
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Wednesday, December 30, 2009 |
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Researchers
| صباح أحمد باشماخ | Bashammakh, Sabah Ahmed | Researcher | Doctorate | |
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