Extensions of ordered semigroups |
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Authors: | Adam J Hulin |
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Institution: | (1) Mathematics Department, Louisiana State University in New Orleans, 70122 New Orleans, Louisiana, U.S.A. |
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Abstract: | The present note summarizes the author's dissertation 2]. Let S and T be ordered semigroups, the latter with a zero element
O. Let Σ be an ideal extension of S by T determined by a partial homomorphism ϕ of T*=T/O into S. A partial solution is given to the problem of determining all ways of extending the given orders on S and T* to Σ=S U T*. Every such “extending order” (≤) on Σ carries with it a certain “null decomposition” T*=X∪Y (X∩Y=ℴ) of T*, and the existence and behavior of extending orders is discussed in terms of properties of null decompositions of T*. |
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