分配超格

Distributive hyperlattice

目的研究超格的内部结构性质。方法通过引入超格的吸收元、固定元等概念来讨论超格中的分配性。结果超格的吸收元、固定元直积仍为超格直积的吸收元、固定元;子超格的直积仍为超格直积的子超格。结论分配超格的同态像、子超格、直积仍是分配超格;超格中的乘法分配律与加法分配律不等价。

Aim The properties of the structures of hyperlattice were studied.Methods Discussing the distributivity of hyperlattices by introducing the concepts of the absorbing elements and fixed elements.Results The direct products of the absorbing elements and fixed elements were still the absorbing element, fixed element of the direct product of hyperlattices respectively, and the direct product of subhyperlattices was the subhyperlattice of the product of hyperlattices.Conclusion The homomorphism image, subhyperlattice and direct product of distributive hyperlattices are still distributive hyperlattices, the multiplicatively distributive law was not equivalent to the additively distributive law.