By Joseph A. Goguen (auth.), Hélène Kirchner, Wolfgang Wechler (eds.)

ISBN-10: 3540531629

ISBN-13: 9783540531623

This quantity comprises papers provided on the moment overseas convention on Algebraic and good judgment Programming in Nancy, France, October 1-3, 1990.

**Read or Download Algebraic and Logic Programming: Second International Conference Nancy, France, October 1–3, 1990 Proceedings PDF**

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**Additional resources for Algebraic and Logic Programming: Second International Conference Nancy, France, October 1–3, 1990 Proceedings**

**Sample text**

Find a ring homomorphism φ between Z20 and Z18 such that the ker φ≠{0}. Z Let f: Z25→ Z16 be a ring homomorphism find the quotient ring 25 . k er f Let Z36 = {0, 1, 2, …, 35} be the ring of integers modulo 36. Let I = {2, …, 34, 0} and J = {3, 9, …, 33, 0} be ideals of Z36. Find the quotient rings Z36/I and Z36/J. Let Z21 = {0, 1, 2, …, 20}. Find an ideal I of Z21 such that Z21/I is a field. Prove for Z12={0, 1, 2, …, 11}, the ring integers with I = {0, 6}, the quotient ring Z12/ I is not a field.

1, in the ring Z6 = {0, 1, 2, …, 5}, 3 2 ∈ Z6 is such that 3 ≡3 (mod 6) but is an idempotent which is not an S-idempotent of Z6. 2: Let Z10 = {0, 1, 2, …, 9} be the ring of integers modulo 10. Now 2 2 the idempotents in Z10 are 5 and 6 for 5 ≡ 5 (mod 10) and 6 ≡ 6 (mod 10). 6 ≡ 4 (mod 10). 2: Let R be a ring. If R has a S-idempotent then R has atleast 2 nontrivial zero divisors. Proof: Let a ∈ R be a S-idempotent, hence a = a and there exists b ∈ R \ {a, 0, 1} 2 2 such that b = a and ab = b which in turn implies (a – 1) b = 0.

4: Let R be a ring. a ∈ R be a S-idempotent. The S-coidempotents of a in general is not unique. Proof: By an example. 11 the S-co-idempotent of 1 + p4 + p5 is not unique. 12: Let Z105 = {0, 1, 2, …, 104} be the ring of integers modulo 105. (105 = 3 × 5 × 7). The idempotent in Z105 are 15, 21, 36, 70, 85 and 91. It can be verified that all these idempotents are S-idempotents. Now the S-co-idempotent for 15 is 90, for 21 is 84, 36 it is 69 for 70 the S-coidempotent is 35, for 85 it is 20 and for 91 the S-co-idempotent is 14.

### Algebraic and Logic Programming: Second International Conference Nancy, France, October 1–3, 1990 Proceedings by Joseph A. Goguen (auth.), Hélène Kirchner, Wolfgang Wechler (eds.)

by Joseph

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