The Mal’tsev product of two varieties of similar algebras is always a quasivariety. We consider the question of when this quasivariety is a variety. The main result asserts that if \(\mathcal {V}\) is a strongly irregular variety with no nullary operations and at least one non-unary operation, and \(\mathcal {S}\) is the variety, of the same type as \(\mathcal {V}\), equivalent to the variety of semilattices, then the Mal’tsev product \(\mathcal {V}\circ \mathcal {S}\) is a variety. It consists precisely of semilattice sums of algebras in \(\mathcal {V}\). We derive an equational base for the product from an equational base for \(\mathcal {V}\). However, if \(\mathcal {V}\) is a regular variety, then the Mal’tsev product may not be a variety. We discuss various applications of the main result, and examine some detailed representations of algebras in \(\mathcal {V}\circ \mathcal {S}\).

两个相似代数的Mal'tsev乘积始终是拟的。我们考虑什么时候这种准度是多种多样的问题。主要结果断言，如果\（\ mathcal {V} \）是一个很强的不规则变体，没有零运算和至少一个非一元运算，并且\（\ mathcal {S} \）是相同的变体类型为\（\ mathcal {V} \），等效于半格的变化，那么Mal'tsev乘积\（\ mathcal {V} \ circ \ mathcal {S} \）也是多种。它恰好由\（\ mathcal {V} \）中的代数的半格和组成。我们从\（\ mathcal {V} \）的方程式基中得出乘积的方程式基。但是，如果\（\ mathcal {V} \）是常规品种，则Mal'tsev产品可能不是品种。我们讨论了主要结果的各种应用，并研究了\（\ mathcal {V} \ circ \ mathcal {S} \）中代数的一些详细表示。