对合m-半格中特殊元、理想及其范畴性质

Special elements,ideals in involutive m-semilattices and its categorical properties

给出对合m-半格的概念,得到对合m-半格的一系列重要性质。定义合m-半格中2种序关系≪、⊴,讨论对合m-半格中对合运算*与特殊元及≪、⊴的相互关系。利用特殊元构造子对合m-半格,研究对合m-半格中理想和滤子的结构,得到利用元素生成理想和滤子的具体形式,引入对合m-半格范畴的定义,探讨对合m-半格范畴中乘积的具体形式,得到对合m-半格范畴的极限结构,证明对合m-半格范畴是完备的。

The concept of involutive m-semilattices is given,and a series of important properties of involutive m-semilattices are obtained.The two order relationships≪and⊴are defined in involutive m-semilattices,and the interrelationships between the involutive m-semilattices*,special element and≪、⊴are discussed.The subinvolutive m-semilattices are constructed by using special elements.The structures of ideals and filters in involutive m-semilattices are studied,the concrete forms of generating ideals and filters from elements are obtained.The definition of the category of involutive m-semilattices is introduced,and the specific form of the product of the category of involutive m-semilattices is discussed,and the limit structure of the category of involutive m-semilattices is obtained.It is proved that the category of involutive m-semilattices is complete.