We present numerous natural algebraic examples without the so-called Canonical Base Property (CBP). We prove that every commutative unitary ring of finite Morley rank without finite-index proper ideals satisfies the CBP if and only if it is a field, a ring of positive characteristic or a finite direct product of these. In addition, we construct a CM-trivial commutative local ring with a finite residue field without the CBP. Furthermore, we also show that finite-dimensional non-associative algebras over an algebraically closed field of characteristic $0$ give rise to triangular rings without the CBP. This also applies to Baudisch’s $2$-step nilpotent Lie algebras, which yields the existence of a $2$-step nilpotent group of finite Morley rank whose theory, in the pure language of groups, is CM-trivial and does not satisfy the CBP.

我们提供了许多没有所谓的规范基属性（CBP）的自然代数例子。我们证明，每个没有有限指数真理想的有限莫利秩交换酉环满足 CBP 当且仅当它是一个域、正特征环或它们的有限直积。此外，我们构造了一个具有有限剩余域且没有 CBP 的 CM 平凡交换局部环。此外，我们还证明了特征代数闭域上的有限维非关联代数$0$产生没有 CBP 的三角环。这也适用于 Baudisch$2$阶幂零李代数，产生$2$有限莫利秩的步幂零群，其理论在群的纯语言中是 CM 平凡的并且不满足 CBP。