%0 Journal Article
%T New Properties over a New Type of Wreath Products on Monoids
%A Suha Ahmed Wazzan
%J Advances in Pure Mathematics
%P 629-636
%@ 2160-0384
%D 2019
%I Scientific Research Publishing
%R 10.4236/apm.2019.98032
%X In [1], a new consequence of the (restricted) wreath product for arbitrary monoids A and B with an underlying set <sub><img src=\"Edit_4271333c-7870-4d19-a9c2-699582f92280.bmp\" alt=\"\" /></sub>. Let us denote it by <img src=\"Edit_251aceee-2696-4b54-9267-6ddb5771bd7e.bmp\" alt=\"\" />. Actually, in the same reference, it has been also defined the generating and relator sets for <img src=\"Edit_0709490c-2c25-4a71-b7e8-cd30e9be0a69.bmp\" alt=\"\" />, 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).
%K Wreath Product
%K Green¡¯s Relations
%K Left Cancellative Monoids
%K Orthodox Monoids
%K Left (Right) Inverse
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=94765