 for commutative rings with identity |
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| Authors: | John Lawrence Boza Tasic |
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| Affiliation: | University of Waterloo, Department of Pure Mathematics, Waterloo, Ontario, Canada N2L 3G1 ; University of Waterloo, Department of Pure Mathematics, Waterloo, Ontario, Canada N2L 3G1 |
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| Abstract: | Let  ,  ,  ,  ,  be the usual operators on classes of rings:  and  for isomorphic and homomorphic images of rings and  ,  ,  respectively for subrings, direct, and subdirect products of rings. If  is a class of commutative rings with identity (and in general of any kind of algebraic structures), then the class  is known to be the variety generated by the class  . Although the class  is in general a proper subclass of the class  for many familiar varieties  . Our goal is to give an example of a class  of commutative rings with identity such that  . As a consequence we will describe the structure of two partially ordered monoids of operators. |
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| Keywords: | Class operators commutative rings with identity partially ordered monoid |
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