In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set . Let us denote it by . Actually, in the same reference, it has been also defined the generating and relator sets for , and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s).
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![\"\"](\"Edit_4271333c-7870-4d19-a9c2-699582f92280.bmp\")
. Let us denote it by ![\"\"](\"Edit_251aceee-2696-4b54-9267-6ddb5771bd7e.bmp\")
. Actually, in the same reference, it has been also defined the generating and relator sets for ![\"\"](\"Edit_0709490c-2c25-4a71-b7e8-cd30e9be0a69.bmp\")
, and then proved some finite and infinite cases about it. In this paper, by considering the product, we show Green’s relations L and R as well as we present the conditions for this product to be left cancellative, orthodox and finally left (right) inverse(s).
