For arbitrary monoids A and B, in Cevik et al. (Hacet J Math Stat 2019:1–11, 2019), it has been recently defined an extended version of the general product under the name of a higher version of Zappa products for monoids (or generalized general product) \(A^{\oplus B}\)\(_{\delta }\bowtie _{\psi }B^{\oplus A}\) and has been introduced an implicit presentation as well as some theories in terms of finite and infinite cases for this product. The goals of this paper are to present some algebraic structures such as regularity, inverse property, Green’s relations over this new generalization, and to investigate some other properties and the product obtained by a left restriction semigroup and a semilattice.

对于任意mono半群A和B，在Cevik等人中。（Hacet J Math Stat 2019：1-11，2019），最近已对通用产品的扩展版本进行了定义，该名称是针对Monoid（或广义通用产品）的Zappa产品的更高版本的名称\（A ^ {\ oplus B} \）\（_ {\ delta} \领结_ {\ psi} B ^ {\ oplus A} \）并已针对该产品介绍了隐式表示以及有关有限和无限情况的一些理论。本文的目的是提出一些代数结构，例如正则性，逆性质，格林对此新泛化的关系，并研究其他性质以及由左约束半群和半格获得的乘积。