| 1. | Homomorphisms between two sets of fuzzy subsemigroups
两个模糊子半群集合之间的同态 |
| 2. | Two properties of infinite cyclic sub - semigroups
无限循环子半群的两个性质 |
| 3. | One catty of peanuts can be divided into left and right
左边的胚子半斤；右边的胚子半斤。 |
| 4. | Some special subsemigroups of regular semigroups with an inverse transversal was discussed . these subsemigroups play a decisive role in constructing regular semigroups with an inverse transversal
摘要讨论了具有逆断面的正则半群的一些特殊子半群。这些子半群在构造具有逆断面的正则半群中起决定性作用。 |
| 5. | Furthermore , in the second chapter semidirect product of 5 and te is discussed . we have the result that it is also clifford quasi - regular semigroup . besides semidirect product of s and te is semilattice of quasi - groups
进一步，论文又在第h章中讨论了半群s和t的子半群te的半直积及其结构，得出了s和t ”的半直积也是clvj 。 |
| 6. | Finally , we show that is a semilattice of groups congru - ence if and only if ( na ) u is a seminormal subsemigroup on 5 , where pna is a group congruence on the semilattice congruence class sa of 5
在这一章的最后文章绪出了半群s上的半格同燃so上的群同余pno的并i ’ upe成为s上的群的半格同余的充分必要条件为u （ na切oeyoey是s的半正规子半群 |
| 7. | In the second section , we give all the ring congruences on a commutative regular semiring s and show that from the lattice of all full , closed , ideal subsemirings of s to the lattice of all the ring conruences on 5 , there is a lattice isomorphism
首先给出一个交换正则半环上的所有环同余，证明了此半环的所有满的、闭的、理想子半环所形成的格与此半环的环同余格同构。 |
| 8. | Next , in the paper the concepts of fuzzy rough subsemigroups and fuzzy rough ideals in a semigroup are first given . in the sense of intersecting sets , fuzzy rough sets of a fuzzy subsemigroup is proved to be its fuzzy subsemigroup , while that of fuzzy ideal is also proved to be its fuzzy ideal
进而，本文在半群中首次提出了模糊粗糙子半群和模糊粗糙理想的概念，在截集意义下，证明了模糊子半群的模糊粗糙集是模糊子半群，模糊左(右，双)理想的模糊粗糙集是模糊左(右，双)理想。 |
| 9. | And we describe the join r v p of a ring congruence r and an arbitrary congruence p on s . similarly , we discribe all the divisible semiring congruences on a distributive semiring . at last , we give the least distributive lattice congruence on a commutative distributive semiring and an idempotent distributi ve semiring
在第三部分给出一个分配半环上的所有可除半环同余，并且在此半环的满的、闭的、自共轭的理想子半环形成的集合与此半环上的可除半环同余的集合之间建立了一个一一的、保序映射。 |
| 10. | Rough ideals in a semigroup have been studied and the concepts of rough subsemigroups , rough ideals been first introduced by kuroki n . under the condition of the congruence relation , rough sets of a subsemigroup was proved to be its subsemigroup , while that of a left ( right , bisides ) ideal was also proved to be its left ( right , bisides ) ideal . next , rough sets in a group have been studied and the concepts of rough subgroups , rough nornal subgroups been first introduced
Kurokin研究了半群中的粗理想，首次提出了粗子半群和粗理想的概念，证明了在同余关系下，半群的粗糙集是半群，左(右，双)理想的粗糙集是左(右，双)理想。接着，他又研究了群中的粗糙集，首次提出了粗子群和粗正规子群的概念，证明了在群中一固定的正规子群所决定的同余关系下，子群的粗糙集是子群，正规子群的粗糙集是正规子群。 |
