W－理想与W－软代数  

W Ideals and W Soft Algebras

作　　者：王尊全 裴礼文[1] 

机构地区：[1]湖北宜昌师专,武汉大学数学系

出　　处：《模糊系统与数学》1995年第3期59-64,共6页Fuzzy Systems and Mathematics

摘　　要：本文给出了Ｗ－理想与Ｗ－软代数的定义，主要结果有（Ⅰ）：（ｄ］，（ｄ＿１］分别是软代数Ｆ的同余理想，ｄ＿１≥ｄ，若（ｄ］是Ｗ－理想，则（ｄ＿１］是Ｗ－理想。（Ⅱ）：分别给出了软代数Ｆ，商软代数Ｆ／θ、软代数的直积Ｆ＝ПＦ＿ｉ是Ｗ－软代数的充分必要条件。In this paper , for a soft algebra(i,e. fuzzy lattice so called also De Morganalgebra), We define that an ideal I is called a W-ideal if there is only one the congruenceθ,shch that the I is a kernel of this congruence θ(i.e. I=kerθ={x|x≡0(θ)}). A softalgebra F is called a W-soft algebra iff all congruence ideals(which are kernels of cer-tain congruences) are W-ideals. Our main results are as following:(1)Let(d]、(d_1] be congruence ideals of a soft algebra F and d_1≥d, (d] is a W-ideal, the(d_1] is also a W-ideal. (2)We get some sufficient and essential conditions such that the soft algebras F、F/θ and П F_i are W-soft algebras respectively.

关 键 词：软代数 同余理想 同余关系 W-理想 W-软代数 

分 类 号：O159[理学—数学]