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Han, Jeong Soon, Kim, Hee Sik, Neggers, J. (1389). Actions, Norms, Subactions and Kernels of (Fuzzy) Norms. نشریه علمی دانشگاه سیستان و بلوچستان, 7(2), 141-147. doi: 10.22111/ijfs.2010.182
Jeong Soon Han; Hee Sik Kim; J Neggers. "Actions, Norms, Subactions and Kernels of (Fuzzy) Norms". نشریه علمی دانشگاه سیستان و بلوچستان, 7, 2, 1389, 141-147. doi: 10.22111/ijfs.2010.182
Han, Jeong Soon, Kim, Hee Sik, Neggers, J. (1389). 'Actions, Norms, Subactions and Kernels of (Fuzzy) Norms', نشریه علمی دانشگاه سیستان و بلوچستان, 7(2), pp. 141-147. doi: 10.22111/ijfs.2010.182
Han, Jeong Soon, Kim, Hee Sik, Neggers, J. Actions, Norms, Subactions and Kernels of (Fuzzy) Norms. نشریه علمی دانشگاه سیستان و بلوچستان, 1389; 7(2): 141-147. doi: 10.22111/ijfs.2010.182

Actions, Norms, Subactions and Kernels of (Fuzzy) Norms

Iranian Journal of Fuzzy Systems
مقاله 11، دوره 7، شماره 2، شهریور 2010، صفحه 141-147    اصل مقاله (199.78 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2010.182
نویسندگان
Jeong Soon Han1؛ Hee Sik Kim* 2؛ J Neggers3
1Department of Applied Mathematics, Hanyang University , Ahnsan, 426-791, Korea
2Department of Mathematics, Hanyang University , Seoul, 133-791, Korea
3Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U. S. A
چکیده
In this paper, we introduce the notion of an action $Y_X$
as a generalization of the notion of a module,
and the notion of a norm $vt: Y_Xto F$, where $F$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: Y_Xto [0, 1]subseteq {bf R}$, with $bf R$  the set of all real numbers. A great many standard mappings on algebraic systems can be modeled on norms as shown in the examples and it is seen that $mathrm{Ker}vt ={y|vt(y)=0}$ has many useful properties. Some are explored, especially in the discussion of fuzzy norms as they relate to the complements of subactions $N_X$ of $Y_X$.
کلیدواژه‌ها
(Fuzzy) norm؛ (Sub) action؛ Kernel
مراجع
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O. T. O'meara, \textrm{Introduction to quadratic forms}, Springer-Verlag, Berlin, 1963.

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J. R. Raftery and T. Sturm, \textit{On completions of pseudo-normed $BCK$-algebras and pseudo-metric universal algebras}, Math. Japonica \textbf{33} (1988), 919-929.

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O. Zariski and P. Samuel, \textrm{Commutative algebra}, D. Van Nostrand, Toronto, \textbf{I, II} (1958).

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