Amalgamations of Partially Ordered Algebraic Structures |
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Page 7
... epimorphism from A to B , and σ a homomorphism from A to C. Then there exists a homomorphism ʼn from B to such that on = σ if and only if homomorphism if P = Φ Го ዋ n is a one - to - one If σ is an epimorphism then so is ŋ , and in ...
... epimorphism from A to B , and σ a homomorphism from A to C. Then there exists a homomorphism ʼn from B to such that on = σ if and only if homomorphism if P = Φ Го ዋ n is a one - to - one If σ is an epimorphism then so is ŋ , and in ...
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... epimorphism from A to A / ̃ . If y is an epimorphism from A to B such that = r , then there is an isomorphism ŋ from Α / Π to B such that n = 9 . Proof . 30 , Proposition 1.3.9 and Corollary 1.3.10 ] . In considering classes of similar ...
... epimorphism from A to A / ̃ . If y is an epimorphism from A to B such that = r , then there is an isomorphism ŋ from Α / Π to B such that n = 9 . Proof . 30 , Proposition 1.3.9 and Corollary 1.3.10 ] . In considering classes of similar ...
Page 15
... epimorphisms , and let ε ( Di n2 , n2 ) © La ( Â3‚č ) . Let gruences r D be the collection of all con- and rn ( Cn2 ) ... epimorphism from D to E. Let Finally , let Բլ = լար and = H2 Բշ * շար Then ( E ; H1 , H2 ) ε H12H2 ) ୮ ...
... epimorphisms , and let ε ( Di n2 , n2 ) © La ( Â3‚č ) . Let gruences r D be the collection of all con- and rn ( Cn2 ) ... epimorphism from D to E. Let Finally , let Բլ = լար and = H2 Բշ * շար Then ( E ; H1 , H2 ) ε H12H2 ) ୮ ...
Contents
Preliminaries Amalgamations in the Class | 4 |
Amalgamations in the Class of Ordered Sets | 17 |
Abelian OGroups | 25 |
3 other sections not shown
Common terms and phrases
₁₂ amalgamation of G Amalgamation Property Archimedian o-groups B. H. Neumann B₁ c₂ cardinal number Cartesian product class of Abelian class of ordered cofinal convex subgroup Corollary define denote divisible Abelian o-groups epimorphism ɛ G free sum Furthermore G and H G in H G into A(S G₁ H₁₂ hence Hn₂ hŋ₁ homomorphism hµ₁ iɛI implies inclusion map interval of g isomorphism kn₂ kµ₂ l-subgroup lattice ordered groups Lemma Let G Let H minimal element mod q n₂ natural embedding nonzero interval o-permutation ordered subgroup ordered subset ordinal partial algebras partially ordered set polyadic equality algebras positive element prime subgroup Proof Proposition 4.21 regular cardinal representing set set of amalgamations similar partial algebras standard amalgamation strong intersection property subgroup of H suppose Theorem 6.9 totally ordered weak intersection property whence zero interval α α