Amalgamations of Partially Ordered Algebraic Structures |
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Page 30
... extends the given - valuation . Proof . We first show existence by defining , for each 8 ε A Gg - G0 = ~ ( G1 | ver ̧ and 8 < ε < Y ) γ ) and mapping 8 → ( Gg a Clearly ( Al ) and ( A3 ) are satisfied . To verify ( A2 ) , let 8 and 8 ...
... extends the given - valuation . Proof . We first show existence by defining , for each 8 ε A Gg - G0 = ~ ( G1 | ver ̧ and 8 < ε < Y ) γ ) and mapping 8 → ( Gg a Clearly ( Al ) and ( A3 ) are satisfied . To verify ( A2 ) , let 8 and 8 ...
Page 34
... given valuation of H to an A- valuation of H , and extend the given A- valuation of K to an A - valuation of K. β H3 G and G2 = H2G , each of the maps a - ( ENG α Since GB HG ) and = απ ( KNG KG ) is an A- valuation of G which extends ...
... given valuation of H to an A- valuation of H , and extend the given A- valuation of K to an A - valuation of K. β H3 G and G2 = H2G , each of the maps a - ( ENG α Since GB HG ) and = απ ( KNG KG ) is an A- valuation of G which extends ...
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