【摘要】：本文給出了反軟子格、格的反軟理想、格的新型軟素理想、格的軟同余的概念,并討論它們的等價條件和一些相關(guān)的性質(zhì)。取得的主要結(jié)果概括如下:在第三章中,先給出反軟子格的概念以及兩個反軟子格分別在限制并和或的運算下仍然是反軟子格。然后得到它的一些等價刻畫。另外還研究了反軟子格同態(tài)像、同態(tài)原像的性質(zhì)。最后在全體反軟子格組成的集合H上引入鏈條件并討論H是阿丁的或諾特的充要條件。在第四章中,首先給出格的反軟理想新概念。然后討論兩個反軟理想分別在限制并、或運算下仍然是反軟理想。最后在全體反軟理想組成的集合H上引入鏈條件并討論H是阿丁的或諾特的充要條件。在第五章中,將參數(shù)集賦予格的代數(shù)結(jié)構(gòu),給出格的新型軟素理想的概念。然后利用擴張原理討論格的新型軟素理想的像與原像的性質(zhì)。最后在全體新型軟素理想組成的集合H上引入鏈條件,并獲得H是阿丁的或諾特的充要條件。在第六章中,給出格上軟同余的新定義。其次討論了它的限制交和且的運算性質(zhì)。最后討論由同余θ及軟同余F誘導(dǎo)的軟同余在商格L/θ下仍是軟同余的性質(zhì)。
[Abstract]:In this paper, the concepts of anti-soft sublattices, anti-soft ideals of lattices, new soft prime ideals of lattices, soft congruences of lattices are given, and their equivalent conditions and some related properties are discussed. The main results obtained are summarized as follows: in Chapter 3, the concept of anti-soft sublattice and the two anti-soft sublattices are still anti-soft sublattices under the operation of restricted sum or respectively. Then some equivalent characterizations of it are obtained. In addition, the properties of the homomorphism image and homomorphic primitive image of anti-soft sublattice are studied. Finally, the chain condition is introduced on the set H of all anti-soft sublattices and the necessary and sufficient conditions for H to be Aden or Nott are discussed. In chapter 4, we first give a new concept of anti-soft ideal. Then it is discussed that two anti-soft ideals are still anti-soft ideals under restricted and or operation respectively. Finally, the chain condition is introduced on the set H of all anti-soft ideals and the necessary and sufficient conditions for H to be Aden or Nott are discussed. In chapter 5, the algebraic structure of lattice is given by parameter set, and the concept of new soft prime ideal is given. Then the properties of the image and the original image of the new soft prime ideal of lattice are discussed by using the extension principle. Finally, the chain condition is introduced on the set H of all new soft prime ideals, and the necessary and sufficient conditions for H to be Aden or Nott are obtained. In Chapter 6, a new definition of soft congruence is given. Secondly, the operation properties of the restricted intersection sum and its operation are discussed. Finally, the property that soft congruence induced by congruence 胃 and soft congruence F is still soft congruence under quotient lattice L / 胃 is discussed.
【學(xué)位授予單位】：江南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O159

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