论文标题
零产物平衡代数
Zero-product balanced algebras
论文作者
论文摘要
我们说，如果$ ab \ otimes c $和$ a \ otimes bc $同意元素的元素张量，则代数为零，如果$ ab \ otimes c $ \ otimes c $和$ a \ otimes a \ otimes a \ otimes a \ otimes a \ otimes cum a \ otimes cum as a \ otimes cum as a \ otimes cum as a \ otimes cum as a \ otimes a \ otimes cut the-otruct a \ otimes c $ a \ otimes co.这与Brešar，Grašič和Ortega的零产物确定的代数的零产物的概念密切相关，但更笼统。从零产物平衡代数的每个过滤性的，零产品保存图都是加权的表达，这意味着零产物平衡的代数由线性和零产物结构确定。此外，可以用方形零元素来描述零产物平衡代数的换向子空间。 我们表明，只有当iDempotent生成时，半电机的交换代数是零产物的平衡。因此，每个交换性零产物平衡的代数都被尼尔氏和势力元素跨越。 我们推断出一个二分法，用于零产物平衡的代数：他们要么接受角色，要么由尼尔植物产生。
We say that an algebra is zero-product balanced if $ab\otimes c$ and $a\otimes bc$ agree modulo tensors of elements with zero-product. This is closely related to but more general than the notion of a zero-product determined algebra of Brešar, Grašič and Ortega. Every surjective, zero-product preserving map from a zero-product balanced algebra is automatically a weighted epimorphism, and this implies that zero-product balanced algebras are determined by their linear and zero-product structure. Further, the commutator subspace of a zero-product balanced algebra can be described in terms of square-zero elements. We show that a semiprime, commutative algebra is zero-product balanced if and only if it is generated by idempotents. It follows that every commutative, zero-product balanced algebra is spanned by nilpotent and idempotent elements. We deduce a dichotomy for unital, zero-product balanced algebras: They either admit a character or are generated by nilpotents.
