maximal algebra 中文意思是什麼
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It is shown that if l is a modular lattice with finite length, and with 0, 1 the least and the largest elements in l respectively, then 1 is the union of some minimal elements in l if and only if 0 is the intersection of some maximal elements in l, if and only if each non - zero element in l is the union of some minimal elements in l. by using these results, we give the necessary and sufficient conditions of an algebra module, module, ring, group and semigroup, respectively, to be semisimple
最後得出有限生成的ps -系是noetherian （ artinian ）系的充要條件是它關于本質子系滿足升鏈（降鏈）條件。第二章給出了一個模格是半單的若干充要條件。得到：有有限長度的模格l上，最大元1是若干極小元的並當且僅當最小元0是若干極大元的交，當且僅當l中任意非零元可表示為若干極小元的並。 -
The basic properties of matrix subalgebra were investiaged, the matrix subalgebra was generated by a single matrix, all maximal ideals were classified, the necessary and sufficient conditions for the subalgebra to be semisimple algebra were given
摘要研究了由一個矩陣生成的拒陣子代數的基本性質，給出了其極大理想的完全分類及這類子代數是半單代數的充要條件。 -
In the third part, this paper studies the mp filters of mtl algebras from many respects. it gives the definition of maximal mp filters, provides the equivalent condition of maximal mp filters, depicts the structure of the subalgebras of mtl algebras, discusses locally finite mtl algebras ; studies the boolean filters of mtl algebras, proves if f is a boolean filters of m which is an mtl algebra, then m / - f is a boolean algebra and discusses local mtl algebras
第三章：從多方面研究了mtl代數的mp濾子，給出mtl代數極大mp濾子的定義；找出了是mtl代數極大mp濾子的等價條件；對mtl代數的子代數給予刻劃；還討論了局部有限mtl代數；研究了mtl代數的布爾濾子；證明了當f是mtl代數m的布爾濾子時， m f是布爾代數；還討論了局部mtl代數。
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