【摘要】：首先給出了格的反軟理想新概念,證明2個(gè)反軟理想分別在軟集的限制并和"或"運(yùn)算下仍然是反軟理想.其次,利用軟集的反對(duì)偶給出反軟理想的等價(jià)刻畫.再次,利用軟集的反擴(kuò)張?jiān)斫o出反軟理想在同態(tài)映射下反像與原像的性質(zhì).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.
[Abstract]:In this paper, we first give a new concept of anti-soft ideals of lattices, and prove that two anti-soft ideals are still anti-soft ideals under the constraints of soft sets and "or" operations, respectively. Secondly, we give the equivalent characterizations of anti-soft ideals by using the anti-couple of soft sets. Thirdly, by using the anti-extension principle of soft sets, the properties of anti-soft ideals under homomorphic mapping are given. Finally, on the set H of all anti-soft ideals, the chain condition is introduced and the necessary and sufficient conditions for H to be Aden or Nott are discussed.
【作者單位】： 江南大學(xué)理學(xué)院信息與計(jì)算科學(xué)系;無(wú)錫城市職業(yè)技術(shù)學(xué)院基礎(chǔ)課部;
【基金】：江蘇省自然科學(xué)基金資助項(xiàng)目(BK20151117) 國(guó)家自然科學(xué)基金資助項(xiàng)目(61673193)
【分類號(hào)】：O159;O153.1
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本文編號(hào)：2397685