By Alexander Barg (auth.), Teo Mora, Harold Mattson (eds.)

This booklet constitutes the strictly refereed lawsuits of the twelfth overseas Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-12, held in Toulouse, France, June 1997.

The 27 revised complete papers awarded have been rigorously chosen by way of this system committee for inclusion within the quantity. The papers deal with a vast diversity of present concerns in coding conception and desktop algebra spanning polynomials, factorization, commutative algebra, genuine geometry, team conception, and so forth. at the mathematical part in addition to software program platforms, telecommunication, complexity conception, compression, sign processing, and so forth. at the laptop technology and engineering side.

**Read or Download Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 12th International Symposium, AAECC-12 Toulouse, France, June 23–27, 1997 Proceedings PDF**

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**Extra resources for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 12th International Symposium, AAECC-12 Toulouse, France, June 23–27, 1997 Proceedings**

**Example text**

Y ( A such that xy = b is a r e g u l a r (3) A ®R Q is the full Proof. (1) = > is a r e g u l a r (1). If x is a r e g u l a r of A. element of A, then Ax ideal of R by y ~ A such that yx = b is a r e g u l a r of R. (1). of J. By Let J be a r e g u l a r (2) there J O R is a r e g u l a r (2) = > (3). of A, then X = z/x, (2) t h e r e ideal is an e l e m e n t H e n c e k = z y / x y = zy/b. t h e r e is an e l e m e n t 1/x = y/b. 2. ring of q u o t i e n t s element of A. b o t h b and y are r e g u l a r expression ring of q u o t i e n t s Let x be a r e g u l a r element y ¢ A and a r e g u l a r J A R is a r e g u l a r in the for k shows that of A.

17. Let A be a torsion d i v i s i b l e R-module. a sum of Artinian divisible Proof. Corollary R-modules. 3.

Be a chain of divisible c HomR(K,D2) c ... 7. by the proof of (3) ~ > H-module HomR(K,Dm) c of D. 6. Thus there is an index m 0 such that = HomR(K,Dmo ) for all m _> m O. 3, p r o v i n g Therefore D m = Dm0 for all that D has ACC on divisible submod- ules. (6) -~-> (I). 3 there is an R - h o m o m o r p h i s m Since K is Artinian submodule by (3) = > and hence f(K) c A. (7). This is a trivial (7) = > (5). It is a consequence R-modules. submodules, Suppose divisible We assert divisible submodule implication.