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DIRECTLY INDECOMPOSABLE RESIDUATED LATTICES | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 3، دوره 6، شماره 2، شهریور 2009، صفحه 7-18 اصل مقاله (184.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2009.204 | ||
| نویسنده | ||
| Lavinia Corina Ciungu* | ||
| Polytechnical University of Bucharest, Splaiul Independentei 313, Bucharest, Romania | ||
| چکیده | ||
| The aim of this paper is to extend results established by H. Ono and T. Kowalski regarding directly indecomposable commutative residuated lattices to the non-commutative case. The main theorem states that a residuated lattice A is directly indecomposable if and only if its Boolean center B(A) is {0, 1}. We also prove that any linearly ordered residuated lattice and any local residuated lattice are directly indecomposable. We apply these results to prove some properties of the Boolean center of a residuated lattice and also define the algebras on subintervals of residuated lattices. | ||
| کلیدواژهها | ||
| residuated lattice؛ Complementary factor congruence؛ Boolean center؛ directly indecomposable algebra؛ Subdirectly irreducible algebra؛ Normal filter | ||
| مراجع | ||
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