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Some results of the semi- mode theory

Author: YangXiaoPeng
Tutor: ChenYuQun
School: South China Normal University
Course: Basic mathematics
Keywords: Balanced mapping Bilinear map Balanced tensor product Bilinear tensor product Annihilator Tensor product of annihilator Faithful Completely faithful
CLC: O153.3
Type: Master's thesis
Year: 2007
Downloads: 12
Quote: 1
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Abstract


Semiring algebraic structure is a common , semi- ring is a commonly used technique by mold half , and half die nature and half die faithful , so research half die faithful plays an important role . This paper is divided into three chapters focus on the the half die annihilator its nature and half die fidelity . The first chapter introduces the R - balanced mapping mold and the concept and nature of the R- bilinear mapping both common mapping and balanced tensor product exported by both mapping and bilinear tensor product proved when R is unital binding commutative ring , balanced tensor product and bilinear tensor product is isomorphic . The second and third chapters is the main part of this paper . Series nature , on the annihilator deduced after about the concept of the tensor product annihilator in the introduction of the the mold half annihilator , such as half die annihilator in semi - mode single-state , full -state isomorphism of under the variation . Tools next annihilator use the annihilator nature as to discuss the semi- die faithfully and completely loyal , got some properties , such as semi- mode direct product with the straight and half die faithful on the tensor product faithfully and completely faithful to such a variety of ways portrayed semi - die faithful , loyal and completely faithful sexual tensor product . Finally, we prove the free half of the mold in the semi - module category generate promoter and generated on sub faithful .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Abstract algebra ( Algebra ) > Ring Theory
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