| 1. | In other words, f respects addition, multiplication and identity element .
换言之，F保持加，乘法和单位元。 |
| 2. | If we consider the integers with ordinary multiplication we have closure, associativity, and identity element .
如果我们考虑整数集且用通常的乘法，我们有封闭性，可结合性，和一个单位元。 |
| 3. | The identity of completely - regular semigroup rings
正则半群环的单位元 |
| 4. | In other words , f respects addition , multiplication and identity element
换言之， f保持加，乘法和单位元。 |
| 5. | The present paper presents a commutativity theorem of rings with identity
摘要给出有单位元的环的一个交换性定理。 |
| 6. | Let k be an algebraically closed field and a be a commutative associative algebra with an identity element 1
设a是代数闭域k上具有单位元1的交换结合代数， d是由a的可交换的k -导子所张成的k -线性空间。 |
| 7. | Throughout this paper , we assume that a and b are rings with identities and the only idempotents in a and b are 1 and 0
设a ， b是两个有单位元的环，并且他们都只有平凡的幂等元， m为非零的( a ， b ) -双模。 |
| 8. | But the results above all base on the fact that semigroups have identity elements . thus it is relatively has certain confinement
但以上的结果都建立在半群含有单位元的这个基础上，这相对就有一定的局限性。 |
| 9. | 3 . considering the longitudinal interaction between soil and single pile , theoretical solution for settlement of the unit cell is obtained
考虑桩与基土的纵向相互作用，推导了深搅桩复合地基单位元沉降的理论解答。 |
| 10. | In order to break the confinement , in this paper we manage to study semidirect products of semigroups regardless of identity elements . that is , we get rid of the especially important condition that semigroups have identity elements
为了突破这一局限性，本文就力争在一般的半群上研究其半直积，即去掉单位元这个特别重要的条件。 |
