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α-type short modules
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نویسنده
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shirali nasrin ,kavoosi ghafi hooriy ,javdannezhad malek
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منبع
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مدل سازي پيشرفته رياضي - 2024 - دوره : 14 - شماره : 3 - صفحه:41 -53
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چکیده
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In this paper, we rst consider the concept of type noetherian dimension of a module such as m, which is the dual of type krull dimension, denoted by tn-dimm,and dened to be the codeviation of the poset of the type submodules of m, then wedualize some of the basic results of type krull dimension for type noetherian dimension.in the following, we introduce the concept of -type short modules (i.e., for each typesubmodule n of m, either n-dim mn or tn-dimn and is the least ordinalnumber with this property), and extend some of the basic results of -short modules to -type short modules. in particular, it is proved that if m is an -type short module,then it has type noetherian dimension and tn-dimm = or tn-dimm = + 1.
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کلیدواژه
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type noetherian dimension ,-type atomic modules ,-type short modules ,-almost type noetherian modules
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آدرس
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shahid chamran university of ahvaz, faculty of mathematical sciences and computer, department of mathematics, iran, shahid chamran university of ahvaz, faculty of mathematical sciences and computer, department of mathematics, iran, shahid rajaee teacher training university, department of mathematics, iran
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پست الکترونیکی
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s.m.javdannezhad@gmail.com
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α-type short modules
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Authors
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Abstract
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in this paper, we rst consider the concept of type noetherian dimension of a module such as m, which is the dual of type krull dimension, denoted by tn-dimm, and dened to be the codeviation of the poset of the type submodules of m, then we dualize some of the basic results of type krull dimension for type noetherian dimension.in the following, we introduce the concept of -type short modules (i.e., for each typesubmodule n of m, either n-dim mn or tn-dimn and is the least ordinalnumber with this property), and extend some of the basic results of -short modules to -type short modules. in particular, it is proved that if m is an -type short module,then it has type noetherian dimension and tn-dimm = or tn-dimm = + 1.
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Keywords
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type noetherian dimension ,-type atomic modules ,-type short modules ,-almost type noetherian modules
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