/usr/share/axiom-20170501/src/algebra/ENTIRER.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | )abbrev category ENTIRER EntireRing
++ Description:
++ Entire Rings (non-commutative Integral Domains), a ring
++ not necessarily commutative which has no zero divisors.
++
++ Axioms\br
++ \tab{5}\spad{ab=0 => a=0 or b=0} -- known as noZeroDivisors\br
++ \tab{5}\spad{not(1=0)}
EntireRing() : Category == SIG where
SIG ==> Join(Ring,BiModule(%,%)) with
noZeroDivisors
++ if a product is zero then one of the factors
++ must be zero.
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