TY  - JOUR
T1  - Decompositions of multiplicative semigroups of m-domain rings and reduced Rickart rings
AU  - Cremer, Insa
PY  - 2025
DA  - January
Y2  - 2024
DO  - 10.24330/ieja.1554197
JF  - International Electronic Journal of Algebra
JO  - IEJA
PB  - Abdullah HARMANCI
WT  - DergiPark
SN  - 1306-6048
SP  - 273
EP  - 296
VL  - 37
IS  - 37
LA  - en
AB  - The main result of this article is that the multiplicative semigroup of an m-domain ring is a strong semilattice of certain subsemigroups, each of which turns out to be a \rcancellative\ monoid, and that this presentation of the semigroup as a strong semilattice of \rcancellative\ semigroups is essentially unique. As a consequence, it is shown that, given an m-domain ring $ \ang{R,+,\cdot} $ with the unary operation $ \dop{} $ mapping every element to its minimal idempotent duplicator (in the sense of N.V.~Subrahmanyam), the algebra $ \ang{R,\cdot,\dop{}} $ is a strong semilattice of \rcancellative\ \dsemigroup s (in the sense of T.~Stokes), also essentially unique. Implications for reduced Rickart rings, which can be seen as a subclass of m-domain rings, are also described.
KW  - Reduced Rickart ring
KW  - m-domain ring
KW  - strong semilattice
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UR  - https://doi.org/10.24330/ieja.1554197
L1  - https://dergipark.org.tr/en/download/article-file/4232479
ER  -