Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-finitely based monoids   We present a general method for proving that a semigroup is non-finitely
based. The method is strong enough to cover the non-finite basis arguments in
articles [1,3,4,5,7,8, 11,14,16,21,27,31,36,37]. In particular, the method
allows to generalize the results in [1,8,36,37] and to simplify their proofs.
The method also allows to remove one of the requirements on the "special system
of identities" used by P. Perkins in [16] to find the first two examples of
finite non-finitely based semigroups. We use our method to prove eleven new
sufficient conditions under which a monoid is non-finitely based. As an
application, we find infinitely many new examples of finite finitely based
aperiodic monoids whose direct product is non-finitely based.

30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex