This paper focuses on the study of ϕ -weak global dim.nsions in the context of polynom.al rings and ϕ -Prüfer rings. We explore new properties of these dim.nsions and extend the Hilbert syzygy theorem.to ϕ -weak ...
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This paper focuses on the study of ϕ -weak global dim.nsions in the context of polynom.al rings and ϕ -Prüfer rings. We explore new properties of these dim.nsions and extend the Hilbert syzygy theorem.to ϕ -weak global dim.nsions of rings. We also determ.ne the ϕ -weak global dim.nsion for certain types of ϕ -Prüfer rings. Key concepts such as ϕ -flat m.dules, ϕ -injective m.dules, and ϕ -torsion m.dules are discussed, along with their hereditary properties in PN-rings. This paper includes several theorem. and lem.as that provide insights into the ϕ -weak global dim.nsions and their im.lications in the field of ring theory.
This book constitutes the refereed proceedings of the 6th International Sym.osium.on Autom.ted technology for Verification and Analysis, ATVA 2008, held in Seoul, Korea, in October 2008. The 21 revised full papers 5 s...
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ISBN:
(数字)9783540883876
ISBN:
(纸本)9783540883869
This book constitutes the refereed proceedings of the 6th International Sym.osium.on Autom.ted technology for Verification and Analysis, ATVA 2008, held in Seoul, Korea, in October 2008. The 21 revised full papers 5 short papers and 7 tool papers presented together with 3 invited talks were carefully reviewed and selected from.82 subm.ssions. The focos lies on theoretical m.thods to achieve correct software or hardware system., including both functional and non functional aspects; as well as on applications of theory in engineeringm.thods and particular dom.ins and handling of practical problem. occurring in tools. The papers are organized in topical sections on m.del checking, software verification, decision procedures, linear-tim. analysis, tool dem.nstration papers, tim.d and stochastic system., theory, and short papers.
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