| 1. | Properties and structure of multiplicative band semirings
乘法带半环的性质和结构 |
| 2. | In this paper we mainly discuss structures and congruences on some semirings
本文主要讨论某些半环的结构与同余。 |
| 3. | In this paper , we mainly discuss structures and properties of some semirings
本文，主要讨论某些半环的构造及性质 |
| 4. | Theorem 1 . 2 . 5 a semiring s is a normal a - idempotent semiring , if and only if s is a strong right normal idempotent semiring of left zero idempotent semirings
5半环s是正规a -幂等半环，当且仅当s是左零幂等半环的强右正规幂等半环。定理1 |
| 5. | Theorem 2 . 2 . 4 a semiring s is an additive normal c - idempotent semiring , if and only if s is a pseudo - strong right normal idempotent semiring of left zero semirings
4s是加法正规c一幂等半环，当且仅当s是左零半环的伪强右正规幂等半环定理2 |
| 6. | Theorem 3 . 3 s is a " d - idempotent semiring , then s is an additive normal idempotent semiring , if and only if s is a pseudo - strong right normal idempotent semiring of left zero semirings
3s是d一幂等半环，则s为加法正规幂等半环，当且仅当s是左零半环的伪强右正规幂等半环 |
| 7. | Theorem 1 . 3 . 3 5 is an a - idempotent semiring , then 5 is a normal idem - potent semiring , if and only if s is a strong semilattice idempotent semiring of rectangular idempotent semirings
定理j设s是人一幂等半环，则s是正规幂等半环，当且仅当s是矩形幂等半环的强半格幂等半环 |
| 8. | And by this we have the structure of the normal idempotent semiring which satisfies the identity ab + b = a + b arises as a strong right normal idempotent semiring of left zero idempotent semirings , and some corollaries
利用这一结构证明了满足等式ab + b = a + b的正规幂等半环是左零幂等半环的强右正规幂等半环，及相关推论。 |
| 9. | Furthermore , structure a kind of commutative semirings . namely fractional semiring . then , we prove a universal property of fractional semiring , and we discuss the relations between the ideals of commutative semirings and the ideals of fractional semirings
然后，我们证明了分式半环的泛性质，并且讨论了分式半环与交换半环理想之间的关系 |
| 10. | 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。 |
