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K- algebra and its conversion in order filtration Groebner bases in both the graded algebra

Author: MaYingCang
Tutor: LiHuiShi；CaoHuaiXin
School: Shaanxi Normal University
Course: Basic mathematics
Keywords: order filtration graded algebra Rees algebra sovable polynomial algebra Groebner basis
CLC: O153
Type: Master's thesis
Year: 2000
Downloads: 45
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Abstract


B.Buchberger 1965 introduction of Groebner base method has proven to be commutative algebra and algebraic geometry in the field of exchange of a powerful computational tool , especially for the exchange of some well-known theory of algorithms have been implemented on the computer. Later, this theory has been successfully extended to the non-commutative algebra. Such as : Free algebra , Weyl algebra , Lie algebra and its enveloping algebra , solvable polynomial algebra and become a tool to solve one of the problem. Research on non- commutative algebra algebra is an important aspect of many important non- commutative algebra has become an important research tool in many branches of mathematics , physics and mechanics theory. Introducing algebra filters and graded algebra associated with Rees algebra is an important means to study non-commutative algebra , compared to non-commutative Groebner base concrete realization of non- commutative algebra algorithms provide a basis for the study , so that many problems can be algorithm. The purpose of this paper is to give non-commutative K- algebra and its conversion with it in order filtration both graded algebra Groebner bases , thus providing a theoretical basis for the study of non-commutative algebra. And computability of Groebner bases , which has a broad prospect in theory and practice . In this paper, K- algebra A, discuss it in a more broad -order filters phasor contact graded algebra gr C (A) and Rees algebra ( ? ) Some properties and get A relations gr C (A) and ( ? ) between the Groebner base paper proved by the definition of the relationship between a 's can get gr C (A) and ( ? ) define relationships to determine their structure. For solvable polynomial algebra , prove it in this order filtration phasor contact graded Rees algebra and algebra are solvable polynomial algebra. Listed below are some of the main results , first introduced Y Graded and mixed order on A . Let K be a fixed domain , {X, Y} = {x 1 , x 2 , ......, x m 1 , y 1 , y 2 , ......, y n } (m, n ∈ N) is a non-empty variable yuan set for convenience , write Z = {z 1 , z 2 , ..., z m + n }, where z i < / sub> = x i , z mj = y j , 1 ≤ j ≤ m, 1 ≤ j ≤ nS = (X, Y ) by X, Y generated unital freedom semigroup 1 , by the above notation known S = lt; Z gt;. So K lt; S gt; as S on K generated in free association K- algebra K lt;. S gt;. Available on the following definition of a graded structure on Y variables to d (ω) is called , said S the length of the element containing the letter ω Y (i.e., the subscript Z is greater than the length m of the alphabet ) , is defined : K lt; S gt; p = {Σc ω ω | c ω ∈ K, ω ∈ S}, p ≥ 0. d (ω) = p1 mix order is defined as follows : I. 1.5 Definitions ( mixed order ) VU, UE; 9, said U by mixing sequence . 1 . At 11 means: or *> Y *. l;,;;, l, or W = t) yH, with y> X. , ; . . X, either. Y = Yy and yX = XX days have u> l. . l. l for l <. Or l. . . . Where > Y-. ; . l; into , when the word refers to only consider the arguments contained in Y on Y graded lexicographic . . . Bu ; ; . ; ; ; . Similar ( see cited .1 ) . 1.1.6 Theorem defined above sequence is a mixed monomial order · The first chapter Y Graded and mixed sequence for discussing K- algebra book plus h er base theory defined above . The second chapter discusses the order filtration K- algebra and its corresponding Homogeneous , see the following definition: 2.2.1 define I. For each FEK <) IL] We note A = an F). One small (F) means J. ' I = million in orders to which I have . PL corpse on t retreat called Homogeneous · + . * Each fe KK} if f = fi; Ten + ... + fp, which rP fi is a face on the Y as V White fractionated defined homogeneous part of the white d @ Tony in K (S) bite . . Mutual Diao white homogeneous element j \f (} generated by a bilateral buried Ku Chuan want , then do I plant ml of about t * - . homogeneous set of ideals { J is a person * ICKu) generated magic Yang bilateral ideal algebra a defined relationships: people = 0,6 EJ then A is a combination of K- algebra , and a = K the mountains, the second chapter shows , K hill order filtration induced order filtration on cA-A ( China a).. . , three ; , where two people A = (q KK BU 1 ) eight, P> 0 in fact , order filtration CA = {qA} * three ( ; Yes * algebra A two K / 1

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