# Looking for a Recommendation on an Abstract Algebra Text [duplicate]

During these days, I have been reading some books concerning algebraic geometry. But I learned commutative algebra two years ago, I cannot remember some basic things such as the definition of irreducible ideals.

Can anyone recommend me a rigorous book to help me recover those old knowledge? I hope it's a book in GTM series.

Thanks.

## marked as duplicate by rschwieb abstract-algebra StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jul 29 at 19:32

• The following link may help you, although I know this is not what you are asking for. math.stackexchange.com/questions/255063/… – NoChance Jul 29 at 3:00
• I was only able to add five duplicates, although I had a lot more queued up. Just putting "[book-recommendation] gallian" into the search field brought a bunch to the top. The references within should be more than sufficient. And if not those, try the boatload of duplicates I wasn't able to list... just use the search bar. – rschwieb Jul 29 at 19:35

In addition to Joseph Gallian's, Contemporary Abstract Algebra, I would also like to recommend John B. Fraleigh's, A First Course in Abstract Algebra for the more advanced student.

Although it is indeed, an undergraduate text, I found it to be a nice bridge between undergraduate and graduate abstract algebra, as I often consulted it for good, basic, explanations of concepts that were not presented clearly in my graduate text.

One of my favorite anecdotes is Fraleigh's take on the number $$\mathbf{1}$$: Unfortunately, $$i$$ has been called an imaginary number and this terminology has led generations of students to view complex numbers with more skepticism than the real numbers. Actually, $$all$$ numbers, such as $$1$$, $$3$$, $$\pi$$, $$-\sqrt{3}$$, and $$i$$ are inventions of our minds. There is no physical entity that is the number $$1$$. If there were, it would surely be in a place of honor in some great scientific museum, and past it would file a steady stream of mathematicians, gazing at $$1$$ in wonder and awe.''