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Semisimple lattices with respect to filter theory
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نویسنده
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. ebrahimi atani s. ,khoramdel m. ,dolati pish hesari s. ,nikmard rostam alipour m.
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منبع
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journal of algebra and related topics - 2022 - دوره : 10 - شماره : 2 - صفحه:131 -143
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چکیده
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Since the theory of filters plays an important role in the theory of lattices, in this paper, we will make an intensive study of the notions of semisimple lattices and the socle of lattices based on their filters. the bulk of this paper is devoted to stating and proving analogues to several well-known theorems in the theory of the rings. it is shown that, if is a semisimple distributive lattice, then is finite. also, an application of the results of this paper is given. it is shown that if is a right distributive ring, then the lattice of right ideals of is semisimple iff is a semisimple ring.
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کلیدواژه
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Lattices Filters Semisimple-lattices
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آدرس
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university of guilan, department of mathematics, Iran, university of guilan, department of mathematics, Iran, university of guilan, department of mathematics, Iran, university of guilan, department of mathematics, iran
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Authors
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