4:["$","div",null,{"className":"min-h-screen bg-white flex flex-col","children":[["$","div",null,{"className":"px-6 pt-6 pb-4 border-b border-gray-100","children":[["$","div",null,{"className":"flex items-center gap-1.5 text-xs text-gray-400 mb-4","children":[["$","a",null,{"href":"/","className":"hover:text-[#26a69a] transition-colors","children":"Market"}],["$","span",null,{"children":"›"}],["$","span",null,{"className":"text-gray-600","children":"Connected ring"}]]}],["$","div",null,{"className":"text-[10px] text-gray-400 uppercase tracking-widest mb-1","children":"Company Profile"}],["$","h1",null,{"className":"text-2xl font-bold text-gray-900","children":"Connected ring"}],null]}],["$","div",null,{"className":"flex-1 px-6 py-6","children":[["$","p",null,{"className":"text-sm text-gray-600 leading-relaxed mb-8","children":"In mathematics, especially in the field of commutative algebra, a connected ring is a commutative ring A that satisfies one of the following equivalent conditions:A possesses no non-trivial idempotent elements;\nthe spectrum of A with the Zariski topology is a connected space."}],["$","div",null,{"className":"columns-1 md:columns-2 gap-10","children":[["$","div","0",{"className":"mb-8 break-inside-avoid","children":[["$","div",null,{"className":"text-xs font-semibold text-gray-400 uppercase tracking-wide mb-3 border-b border-gray-100 pb-1","children":"Examples and non-examples"}],["$","div",null,{"className":"text-sm text-gray-600 leading-relaxed wiki-content","dangerouslySetInnerHTML":{"__html":"Connectedness defines a fairly general class of commutative rings. For example, all local rings and all (meet-)irreducible rings are connected. In particular, all integral domains are connected. Non-examples are given by product rings such as Z × Z; here the element (1, 0) is a non-trivial idempotent. ==Generalizations=="}}]]}],["$","div","1",{"className":"mb-8 break-inside-avoid","children":[["$","div",null,{"className":"text-xs font-semibold text-gray-400 uppercase tracking-wide mb-3 border-b border-gray-100 pb-1","children":"Generalizations"}],["$","div",null,{"className":"text-sm text-gray-600 leading-relaxed wiki-content","dangerouslySetInnerHTML":{"__html":"In algebraic geometry, connectedness is generalized to the concept of a connected scheme. ==References=="}}]]}]]}],["$","div",null,{"className":"mt-8 pt-4 border-t border-gray-100","children":["$","a",null,{"href":"https://en.wikipedia.org/wiki/Connected%20ring","target":"_blank","rel":"noopener noreferrer","className":"text-xs text-gray-400 hover:text-gray-600 transition-colors","children":"Source: Wikipedia ↗"}]}]]}],["$","div",null,{"className":"px-6 py-4 border-t border-gray-100 flex justify-between items-center","children":[["$","a",null,{"href":"/","className":"text-xs text-gray-300 italic hover:text-gray-500 transition-colors","children":"tickerdossier.com"}],["$","a",null,{"href":"https://tickerdossier.substack.com","target":"_blank","rel":"noopener noreferrer","className":"text-xs text-gray-400 hover:text-gray-600 transition-colors","children":"tickerdossier.substack.com"}]]}]]}]