document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195280>Question 1195280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the characteristic of the ring.\r<BR>\n" );
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document.write( "(P(∅), Δ,∩) \r<BR>\n" );
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document.write( "I think it has no characteristic based on the definition.<BR>\n" );
document.write( "In the powerset of the empty set<BR>\n" );
document.write( "additive identity (0)= {}<BR>\n" );
document.write( "multiplicative identity (1)= {}<BR>\n" );
document.write( "so 0=1\r<BR>\n" );
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document.write( "Please help. Thank you.\r<BR>\n" );
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document.write( "These are the definition <BR>\n" );
document.write( "char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0). \r<BR>\n" );
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document.write( "If this sum never reaches the additive identity the ring is said to have characteristic zero.\r<BR>\n" );
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document.write( "The ring of integers modulo n has characteristic n\r<BR>\n" );
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document.write( "If 0=1 it says to have no characteristic. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827722 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=827722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "On characteristic of rings in Algebra see this Wikipedia article\r<BR>\n" );
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document.write( "https://en.wikipedia.org/wiki/Characteristic_(algebra)#:~:text=In%20mathematics%2C%20the%20characteristic%20of,the%20additive%20identity%20(0).\r<BR>\n" );
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document.write( "I do not think that searching/investigating of a characteristic of a ring which is an empty set \r<BR>\n" );
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document.write( "would be of any interest.\r<BR>\n" );
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document.write( "It is the same as if you search for a penny in a pocket while there is no penny there - - - and you know about it . . . \r<BR>\n" );
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document.write( " </SPAN>\n" );
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